Chapter 13
Use the following to answer questions 1-3:
Suppose that the Blood Alcohol Content (BAC) of students who drink five beers varies from
student to student according to a normal distribution with mean 0.07 and standard deviation 0.01.
1. The middle 95% of students who drink five beers have BAC between
A) 0.06 and 0.08. B) 0.05 and 0.09. C) 0.04 and 0.10. D) 0.03 and 0.11.
2. What percent of students who drink five beers have BAC above 0.08 (the legal limit for
driving in most states)?
A) 0.15% B) 2.5% C) 5% D) 16% E) 32%
3. What percent of students who drink five beers have BAC above 0.10 (the legal limit for
driving other states)?
A) 0.15% B) 2.5% C) 5% D) 16% E) 32%
4. SAT scores are normally distributed with mean 500 and standard deviation 100. Julie
scores 650. Her standard score is
A) 150. B) 15. C) 1.5. D) 0.15.
5. A study of grades at a large university finds that the mean GPA for all undergraduates is
2.77. The distribution of grades is roughly normal. To make this description useful we
must also know
A) the correlation. B) the median. C) the slope. D) the standard deviation.
6. Jorge's score on Exam 1 in his statistics class was at the 64th percentile of the scores for
all students. His score falls
A)
between the minimum and the first quartile.
B)
between the first quartile and the median.
C)
between the median and the third quartile.
D)
between the third quartile and the maximum.
Use the following to answer questions 7-10:
The length of pregnancy isn't always the same. In pigs, the length of pregnancies varies
according to a normal distribution with mean 114 days and standard deviation five days.
A)
B)
7. What range covers the middle 95% of pig pregnancies?
109 to 119 days
C)
104 to 124 days
D)
99 to 129 days
94 to 134 days
8. What percent of pig pregnancies are longer than 114 days?
A) 16% B) 34% C) 50% D) 84%
9. What percent of pig pregnancies are longer than 109 days?
A) 16% B) 34% C) 50% D) 84%
10. The median length of a pig pregnancy is
A)
B)
C)
D)
E)
119 days.
114 days.
109 days.
between 109 and 119 days, but can't be more
specific.
greater than 114 days, but can't be more
specific.
11. Two measures of center are marked on the density curve below.
A)
The median is at the solid line and the mean is
at the dashed line.
The median is at the dashed line and the mean
is at the solid line.
The mode is at the dashed line and the median
is at the solid line.
The mode is at the solid line and the median is
at the dashed line.
B)
C)
D)
12. The mean of any density curve is
A)
the point where the curvature of the curve
changes.
the point at which the curve reaches its highest
value.
the point at which the curve would balance if
made of solid material.
the point with half the area under the curve to
its left and half to its right.
B)
C)
D)
Use the following to answer questions 13-14:
13. The mean of the normal curve is
A) 80. B) 90. C) 100. D) 110.
E) 120.
14. The standard deviation of the normal curve is
A) 5.
B) 10.
C) 15.
D) 20.
E) 25.
15. If you know the mean and standard deviation of a distribution, do you know the
complete shape of the distribution?
A)
Yes, always.
B)
Yes if the distribution is normal, but not in
general.
C)
Yes if the distribution is symmetric, but not in
general.
D)
No, never.
16. For a normal distribution with mean 20 and standard deviation 5, approximately what
percent of the observations will be between 5 and 35?
A) 50% B) 68% C) 95% D) 99.7% E) 100%
17. For a normal distribution with mean 20 and standard deviation 5, approximately what
percent of the observations will be less than 20?
A) 50% B) 68% C) 95% D) 99.7% E) 100%
18. For a normal distribution with mean 20 and standard deviation 5, approximately what
percent of the observations will be less than 10?
A) 99.7% B) 97.5% C) 2.5% D) 95% E) 99%
19. You are told that your score on an exam is at the 85th percentile of the distribution of
scores. This means that
A)
your score was equal to or lower than
approximately 85% of the people who took
this exam.
B)
your score was equal to or higher than
approximately 85% of the people who took
this exam.
C)
you answered 85% of the questions correctly.
D)
your score was the same as 85% of the people
who took this exam.
E)
you are 85% confident that your score is
significant.
20. The mean is 80 and the standard deviation is 10. What is the standard score for an
observation of 90?
A) 90 B) 0 C) 10 D) 1.0 E) –1.0
A)
B)
C)
21. A normal distribution always
is skewed to the right. D)
is skewed to the left.
E)
has a mean of 0.
has more than one
peak.
is symmetric.
22. The distribution of heights of adult men is approximately normal with mean 69 inches
and standard deviation 2.5 inches. What percent of all men are (to the nearest inch)
between 67 and 71 inches tall?
A) 27% B) 58% C) 68% D) 73% E) 95%
23. The distribution of heights of adult men is approximately normal with mean 69 inches
and standard deviation 2.5 inches. About what percent of men are shorter than 64
inches?
A) 95% B) 68% C) 16% D) 5% E) 2.5%
24. The distribution of heights of adult men is approximately normal with mean 69 inches
and standard deviation 2.5 inches. How tall is a man whose standardized height is z =
0.3?
A)
68.25 inches
B)
68.7 inches
C)
69.3 inches
D)
69.75 inches
E)
We can't tell without the normal table from the
text.
25. The distribution of heights of adult men is approximately normal. A man whose
standardized height is 0.3 is at the 61.79th percentile. What percent of all men are taller
than he is?
A)
61.79%
B)
38.21%
C)
0.3%
D)
E)
We can't tell from the given information.
We can't tell without the normal table from the
text.
26. Which of the following is least likely to have a nearly normal distribution?
A)
Heights of all female students taking STAT 001
at State Tech.
B)
IQ scores of all students taking STAT 001 at
State Tech.
C)
The SAT Math scores of all students taking
STAT 001 at State Tech.
D)
Family incomes of all students taking STAT
001 at State Tech.
E)
Time from conception to birth of all students
taking STAT 001 at State Tech.
Use the following to answer questions 27-28:
Record the death rate from heart disease per 100,000 people in a group of developed countries.
The distribution is roughly described by this normal curve:
27. From this normal curve, we see that the mean heart disease death rate per 100,000
people is about
A) 60. B) 120. C) 190. D) 250. E) 400.
28. From the normal curve, we see that the standard deviation of the heart disease rate per
100,000 people is closest to
A) 25. B) 65. C) 100. D) 200. E) 400.
A)
B)
C)
D)
E)
29. If your score on a test is at the 60th percentile, you know that your score lies
below the first quartile.
between the first quartile and the median.
between the median and the third quartile.
above the third quartile.
Can't say where it lies relative to the quartiles.
30. The distribution of heights of adult men is approximately normal with mean 69 inches
and standard deviation 2.5 inches. About what percent of men are taller than 74 inches?
A) 95% B) 68% C) 16% D) 5% E) 2.5%
31. The distribution of heights of adult men is approximately normal with mean 69 inches
and standard deviation 2.5 inches. How tall is a man whose standardized height is z =
–0.3 ?
A)
68.25 inches
B)
68.7 inches
C)
69.3 inches
D)
69.75 inches
E)
Can't tell without the normal table from the
text.
32. The distribution of scores on an SAT exam is normal, with mean 500 and standard
deviation 100. So the median score on the exam
A)
is less than 500.
B)
is equal to 500.
C)
is greater than 500.
D)
could be anywhere between 400 and 600.
E)
is unknown—could be either less or greater
than 500.
The following two questions are related to question 33 in Chapter 14.
Use the following to answer questions 33-34:
Scores on the American College Testing (ACT) college entrance exam follow the normal
distribution with mean 18 and standard deviation 6. Wayne's standard score on the ACT was –
1.1.
33. What was Wayne's actual ACT score?
A) 6.6
B) –6.6
C) 11.4
D) 24.6
E) 19.8
34. Wayne's buddy Garth took the SAT. His standard score on the SAT was 0.6. This
means that Garth's actual score was
A)
more than 1 standard deviation below the mean
SAT score.
B)
less than 1 standard deviation below the mean
SAT score.
C)
less than 1 standard deviation above the mean
SAT score.
D)
more than 1 standard deviation above the mean
SAT score.
E)
Can't tell without knowing the standard
deviation.
Use the following to answer questions 35-36:
A)
B)
C)
35. The figure is the density curve of a distribution. This distribution is
roughly symmetric.
D)
positively correlated.
skewed to the left.
E)
negatively correlated.
skewed to the right.
36. Five of the seven points marked on this density curve make up the five-number
summary for this distribution. Which two points are not part of the five-number
summary?
A) B and E B) C and F C) C and E D) B and F E) A and G
37. Your score on the statistics final exam is at the 70th percentile of the scores for the class.
Your score lies
A)
below the lower quartile.
B)
between the lower quartile and the median.
C)
between the median and the third quartile.
D)
above the third quartile.
E)
Can't tell which quarter your score lies in.
38. If the heights of 99.7% of American men are between 5'0" and 7'0", what is your
estimate of the standard deviation of the height of American men? Assume the heights
of American men are approximately normally distributed.
A) 1 inch B) 3 inches C) 4 inches D) 6 inches E) 12 inches
38. Scores on the Graduate Record Examination (GRE) follow a normal distribution.
Jennifer's score is 2 standard deviations above the mean. About what percent of scores
are higher than Jennifer's?
A)
50%
D)
2.5%
B)
16%
E)
Can't tell from the
information given.
C)
5%
40. Scholastic Assessment Test (SAT) scores are normally distributed with mean 500 and
standard deviation 100. Jason scores 440 on the math SAT. Jason's standard score is
A) 0.6. B) –0.6. C) 4.4. D) 60. E) –60.
Use the following to answer questions 41-45:
The weights of dormitory cockroaches follow a normal distribution with mean 80 grams and
standard deviation 2 grams. The figure below is the normal curve for this distribution of weights.
41. At which point on the normal curve is the median of the distribution of cockroach
weights located?
A)
C
D)
Either C or E, but can't
tell which.
B)
D
E)
Can't tell from the
information given.
C)
E
42. Point A on this normal curve corresponds to
A) 68 grams. B) 68 (grams)2. C) 72 grams.
43. Point C on this normal curve corresponds to
A) 84 grams. B) 82 grams. C) 78 grams.
D) 74 grams.
D) 76 grams.
E) 76 grams.
E) 76 (grams)2.
44. About what percent of the cockroaches have weights between 76 grams and 84 grams?
A) 99.7% B) 95% C) 68% D) 47.5% E) 34%
45. About what percent of the cockroaches have weights less than 78 grams?
A) 47.5% B) 34% C) 32% D) 16% E) 2.5%
Use the following to answer questions 46-47:
46. The mean of this normal distribution is
A) about 10. B) about 50. C) about 60.
D) about 70.
47. The standard deviation of the normal distribution is
A) about 10. B) about 20. C) about 70. D) about 100.
48. You can roughly locate the mean of a density curve by eye because it is
A)
the point at which the curve would balance if
made of solid material.
B)
the point that divides the area under the curve
into two equal parts.
C)
the point at which the curve reaches its peak.
D)
the point where the curvature changes
direction.
49. The heights of American men aged 18 to 24 are normally distributed with mean 68
inches and standard deviation 2.5 inches. So half of all young men are taller than
A) 68 inches. B) 70.5 inches. C) 73 inches. D) 75.5 inches.
50. The heights of American men aged 18 to 24 are normally distributed with mean 68
inches and standard deviation 2.5 inches. About 95% of all young men have heights
between
A)
65.5 inches and 70.5
C)
60.5 inches and 75.5
inches.
inches.
B)
63 inches and 73
D)
58 inches and 78
inches.
inches.
51. Which of these distributions is least likely to be normally distributed?
A)
annual salaries of all professors at your college
B)
heights of all female undergraduates at your
college
C)
college board exam scores of all high school
seniors in your state
D)
weights of all cockroaches in your dormitory
52. The 70th percentile of a distribution is
A)
B)
C)
D)
the number with 70% of the data below it.
the number with 70% of the data above it.
the number that is 70% of the average.
70% of the sample size.
53. The standard deviation should not be used to measure spread when
A)
the distribution is
C)
the distribution is
normal.
symmetric.
B)
the mean is used to
D)
the distribution is
measure center.
skewed.
Use the following to answer questions 54-58:
Scores of adults aged 60 to 64 on a common IQ test are approximately normally distributed with
mean 90 and standard deviation 15.
54. Since IQ scores of adults aged 60 to 64 are normally distributed with mean 90 and
standard deviation 15, then about 40% of the scores are between
A)
60 and 120.
D)
the 25th and 75th
percentiles.
B)
45 and 135.
E)
the 30th and 70th
percentiles.
C)
85 and 90.
55. What range of IQ scores contains the central 95% of the population of adults aged 60 to
64?
A) 75 to 105 B) 60 to 120 C) 30 to 150 D) 45 to 135
A)
B)
56. The third quartile of the distribution of IQ scores of adults aged 60 to 64 is
between 90 and 105. C)
between 90 and 75.
between 105 and 120. D)
between 60 and 75.
57. Suppose we call an IQ of 90 "normal" for adults aged 60 to 64. What percent of the
population have "below normal" IQs?
A)
50%
C)
more than 50%
B)
less than 50%
D)
Can't tell from the
information given.
58. About what percent of the population of adults aged 60 to 64 have an IQ lower than 60?
A) 90% B) 20% C) 16% D) 10% E) None of the above.
59. The 35th percentile of a population is the number x such that
A)
35% of the population scores are above x.
B)
65% of the population scores are above x.
C)
65% of the population scores are below x.
D)
x is 35% of the population median.
E)
x is 35% of the population mean.
60. If the mean of a list of numbers is 16.7 and the standard deviation is 0, then
there must have been an arithmetic mistake.
all of the numbers on the list are the same.
the histogram has a single peak at 0.
68% of the numbers on the list are between –
16.7 and +16.7.
E)
68% of the numbers on the list are between 0
and 33.4.
A)
B)
C)
D)
61. The histogram of several hundred observations shows a normal distribution shape. The
smallest observation is 11 and the largest is 89. We can estimate that the standard
deviation of this distribution is approximately
A) 78. B) 39. C) 19.5. D) 13. E) 11.
62. Entomologist Heinz Kaefer has a colony of bongo spiders in his lab. There are 1,000
adult spiders in the colony, and their weights are normally distributed with mean 11
grams and standard deviation 2 grams. About how many spiders in the colony weigh
more than 12 grams?
A) 690 B) 310 C) 160 D) 840 E) 117
63. IQs among undergraduates at Mountain Tech are approximately normally distributed.
The mean undergraduate IQ is 110. About 95% of undergraduates have IQs between 100
and 120. The standard deviation of these IQs is about
A) 5. B) 10. C) 15. D) 20. E) 25.
64. Suppose that adult women in China have heights that are normally distributed with
mean 155 centimeters and standard deviation 8 centimeters. Adult women in Japan
have heights which are normally distributed with mean 158 centimeters and standard
deviation 6 centimeters. Which country has the higher percentage of women taller than
167 centimeters?
A)
China
B)
Japan
C)
The percentages are the same.
D)
It is not possible to tell from the information
given.
65. The scores on the final exam in a statistics course are close to being normally
distributed. The mean score is 60 points, and four-fifths of the class score between 45
and 75. The standard deviation of the scores is
A)
larger than 15 points.
B)
smaller than 15 points.
C)
impossible to say with the information given.
66. If the mean of a list of numbers is 16.7 and the standard deviation is 0, then
there must have been an arithmetic mistake.
all of the numbers on the list are equal to 16.7.
all of the numbers on the list are the same, but
their common value can be anything.
D)
68% of the numbers on the list are between –
16.7 and +16.7.
E)
68% of the numbers on the list are between 0
and 33.4.
A)
B)
C)
Use the following to answer questions 67-69:
Scores on the 2007 SAT writing exam were normally distributed, with mean 495 and standard
deviation about 110.
67. The median score was
A) 110. B) 715. C) 495.
D) Can't be determined without more information.
68. What percent of all students scored between 385 and 605?
A) 68% B) 95% C) 75% D) 99%
69. What percent of all students scored above 605?
A) 32% B) 16% C) 75% D) Can't be determined without more information.
70. What percent of the observations from a normal distribution lie between the standard
scores z = –1 and z = 2? (Hint: sketch a normal curve.)
A) 16% B) 47.5% C) 50% D) 61% E) 81.5%
The following question is related to question 75 in Chapter 12 and 28 in Chapter 16.
71. The Internal Revenue Service examines an SRS of 1,000 income tax returns. The
distribution of incomes shown on these 1,000 tax returns is almost certainly
A)
strongly skewed to the right.
B)
nearly symmetric but not close to normal.
C)
close to normal.
D)
strongly skewed to the left.
72. Scores on the Scholastic Assessment Test are reported on a scale that yields a normal
distribution with mean 500 and standard deviation 100. The percent of scores above
500 on the SAT is
A) 99.7%. B) 95%. C) 68%. D) 50%. E) 34%.
73. Scores on the Scholastic Assessment Test are reported on a scale that yields a normal
distribution with mean 500 and standard deviation 100. Julie scores 600 on the SAT.
Her standard score is
A) z = –1.
B) z = 0.
C) z = 1.
D) z = 6.
E) z = 100.
74. In any normal distribution, the percent of observations falling between standard score
z = 0 and standard score z = 2 is about
A) 95%. B) 81.5%. C) 61%. D) 50%. E) 47.5%.
75. George has an average bowling score of 180 and bowls in a league where the average
for all bowlers is 150 and the standard deviation is 20. Bill has an average bowling
score of 190 and bowls in a league where the average is 160 and the standard deviation
is 15. Who ranks higher in his own league, George or Bill?
A)
Bill, because his 190 is higher than George's
180.
B)
Bill, because his standard score is higher than
George's.
C)
Bill and George have the same rank in their
leagues, because both are 30 pins above the
mean.
D)
George, because his standard score is higher
than Bill's.
76. Scores of adults on the Wechsler Adult Intelligence Scale (a common IQ test) follow a
normal distribution. The middle 95% of scores on this test range from 70 to 130. What
is the standard deviation of the test scores?
A) 20 points B) 15 points C) 10 points D) 7.5 points E) 5 points
77. Until the scale was changed in 1995, SAT scores were based on a scale set many years
ago. For math scores, the mean under the old scale in the 1990s was about 470 and the
standard deviation was about 110. What is the standard score of someone who scored
500 on the old SAT?
A) z = 0.27 B) z = –0.27 C) z = 30 D) z = –30 E) z = 0
78. The change in scales in 1995 (for math scores, the mean under the old scale in the 1990s
was about 470 and the standard deviation was about 110) makes it hard to directly
compare scores on the 1994 Math SAT (mean 470, standard deviation 110) and the 1996
Math SAT (mean 500, standard deviation 100). Jane took the SAT in 1994 and scored
500. Her sister Colleen took the SAT in 1996 and scored 520. Who did better on the
exam, and how can you tell?
A)
Colleen—she scored 20 points higher than
B)
C)
D)
E)
Jane.
Colleen—her standard score is higher than
Jane's.
Jane—her standard score is higher than
Colleen's.
Jane—the standard deviation was bigger in
1994.
Can't tell from the information given.
79. The risk of an investment is measured by the variability of the changes in its value over
a fixed period, such as a year. More variation from year to year means more risk. The
government's Securities and Exchange Commission wants to require mutual funds to tell
investors how risky they are. A news article (New York Times, April 2, 1995) says that
some people think that "the proposed risk descriptions, especially one that goes by the
daunting name standard deviation" are hard to understand. Explain to a friend what the
standard deviation means, using the fact that the changes in a mutual fund's value over
many years have a roughly normal distribution.
A)
The standard deviation is the distance between
the first and third quartiles, so it spans half the
yearly changes in the fund's value.
B)
The standard deviation is the largest change we
ever expect to see in a year.
C)
The yearly change in the fund's value will be
greater than the standard deviation half the
time and less than the standard deviation half
the time.
D)
Start with the average (mean) change in the
fund's value over many years; the actual
change will be within one standard deviation
of that average in about 68% of all years.
E)
Start with the average (mean) change in the
fund's value over many years; the actual
change will be within one standard deviation
of that average in about 95% of all years.
80. Scores on the SAT exams have approximately a normal distribution with mean 500 and
standard deviation 100. Julie scores 400 on the Math SAT. What percent of scores are
higher than Julie's?
A) 16% B) 32% C) 68% D) 84% E) None of these.
81. Jason scores 380 on the Math SAT. (SAT scores have mean 500 and standard deviation
100.) Jason's standard score is
A) –120. B) –1.2. C) 1.2.
D) 3.8.
E) None of these.
82. You are chatting with the principal of a local high school. The topic of SAT scores
comes up, and the principal mentions that SAT scores at the school are normally
distributed. She doesn't remember the mean or the standard deviation, but she does
remember that the first and third quartiles are 500 and 600. The standard deviation of
SAT Verbal scores is closest to
A) 550 points. B) 00 points. C) 75 points. D) 50 points. E) 25 points.
The following question is related to questions 88-89 in Chapter 12.
83. A medical researcher collects health data on
many women in each of several countries. One
of the variables measured for each woman in
the study is her weight in pounds. The
following list gives the five-number summary
for the weights of women in each of several
countries. The first and last numbers for each
country are the deciles (that is, the 10th and
90th percentiles).
Country
A
Country B
Country C
Country D
A) Country A
B) Country B
100
113
84
100
143
135
96
110
182
191
151
110
120
In one of these countries the weights of women
are approximately normally distributed. Which
country is it?
C) Country C D) Country D
Use the following to answer questions 84-87:
Suppose that the distribution of Writing SAT scores from your state this year is normally
distributed with mean 480 and standard deviation 110 for males, and mean 500 and standard
deviation 100 for females.
84. If someone who scores 700 or higher on the Math SAT can be considered exceptional,
the proportion of exceptional students among male SAT takers is about
185
124
160
A) 15%.
B) 5%.
C) 2.5%.
D) 1.5%.
E) 0.15%.
85. The proportion of exceptional students among female SAT takers is __________ the
proportion of geniuses among males who took the test.
A)
greater than
C)
about equal to
B)
less than
D)
Can't tell from the
information given.
86. Mary took the Writing SAT and scored 670. She did better than approximately _____%
of female students taking the test.
A) 99.9 B) 99 C) 97 D) 95 E) 90
87. How well did Mary's score of 670 rate in terms of the scores of male students? Mary
did better than approximately ____% of male students taking the test.
A) 99.9 B) 99 C) 97 D) 95 E) 90
88. A number with 60% of the data above it is
A)
the 60th percentile.
C)
B)
the 40th percentile.
always bigger than the
mean.
always smaller than
the mean.
D)
Chapter 14
The following two questions are related to questions 1-4 in Chapter 12 and 1 in Chapter 15.
Use the following to answer questions 1-2:
The stock market did well during the 1990s. Here are the percent total returns (change in price
plus dividends paid) for the Standard & Poor's 500 stock index:
Year
Return
1990
–3.1
1991
30.5
1992 1993
7.6 10.1
1994
1.3
1995
37.6
1996
23.0
1997 1998
33.4 28.6
1999
21.0
1. The correlation of U.S. stock returns with overseas stock returns during these years was
about r = 0.4. This tells you that
A)
B)
C)
D)
E)
when U.S. stocks rose, overseas stocks also
tended to rise, but the connection was not very
strong.
when U.S. stocks rose, overseas stocks rose by
almost exactly the same amount.
when U.S. stocks rose, overseas stocks tended
to fall, but the connection was not very strong.
there is almost no relationship between
changes in U.S. stocks and changes in overseas
stocks.
nothing, because this is not a possible value of
r.
2. Stock returns are measured in percent. What are the units of the mean, the median, the
quartiles, the standard deviation, and the correlation between U.S. and overseas returns?
A)
all are measured in percent
B)
all are measured in percent except the standard
deviation, which is measured in squared
percent
C)
all are measured in percent except the
correlation, which is a number that has no units
D)
all are measured in percent except the
correlation, which is measured in squared
percent
The next three questions are related to questions 2-3 in Chapter 15.
Use the following to answer questions 3-5:
How well does the number of beers a student drinks predict his or her blood alcohol content?
Sixteen student volunteers at The Ohio State University drank a randomly assigned number of
cans of beer. Thirty minutes later, a police officer measured their blood alcohol content (BAC).
A scatterplot of the data appears below.
3. One student drank 9 beers. You see from the scatterplot that his BAC was about
A) 0.19. B) 9. C) 19. D) 0.05.
4. The scatterplot shows
A)
B)
C)
D)
E)
a weak negative relationship.
a moderately strong negative relationship.
almost no relationship.
a weak positive relationship.
a moderately strong positive straight-line
relationship between number of beers and
BAC.
5. A plausible value of the correlation between number of beers and blood alcohol content,
based on the scatterplot, is
A) r = –0.9. B) r = –0.3. C) r close to 0. D) r = 0.3. E) r = 0.9.
6. Which statistical measure is not strongly affected by a few outliers in the data?
A)
B)
the mean
the median
C)
D)
the standard deviation
the correlation
coefficient
7. Which of these statements about the standard deviation s is true?
A)
s is always 0 or positive.
B)
s should be used to measure spread only when
the mean is used to measure center.
C)
s is a number that has no units of measurement.
D)
Both (A) and (B), but not (C).
E)
All of (A), (B), and (C).
The following two questions are related to question 2 in Chapter 11, 12-13 in Chapter 12, and 910 in Chapter 15.
Use the following to answer questions 8-9:
Here is a stemplot of the percent of males, 15 and older, who are illiterate in 139 countries,
according to the United Nations. For example, the highest illiteracy rate was 69%, in the African
country of Mali.
0 000000000000000011111111111122222233333334444444
0 5555666666666777777899
1 0000000111111244
1 6667788999
2 0000011123333
2 56899
3 011133
3 5789
4 0013
4 77
5 00
5 6779
6 3
6 9
A)
B)
C)
D)
8. Based on the shape of this distribution, what numerical measures would best describe it?
the five-number summary
the mean and standard deviation
the mean and the quartiles
the mean and the correlation coefficient
9. The United Nations also has data on the percent of adult females who are illiterate in
each of these 139 countries. The correlation between male illiteracy rate and female
illiteracy rate is r = 0.95. This tells us that
A)
countries with high male illiteracy tend to also
have high female illiteracy, and the
relationship is very strong.
B)
countries with high male illiteracy tend to also
have high female illiteracy, but the two are
only weakly related.
C)
countries with high male illiteracy tend to have
low female illiteracy, and the relationship is
very strong.
D)
countries with high male illiteracy tend to have
low female illiteracy, but the two are only
weakly related.
E)
there is very little relationship between the
illiteracy rates for males and females.
The following question is related to questions 14-18 in Chapter 12.
10. Here are the number of hours that each of a group of students studied for this exam:
2 4 22 2 1 4 1 5 5 4
A)
B)
C)
D)
E)
Which of the median, mean, third quartile, and standard deviation are measured in
hours?
All four are measured in hours.
All except the standard deviation are measured
in hours.
Only the median and the mean are measured in
hours.
Only the median is measured in hours.
None of the four are measured in hours.
11. To display the distribution of the lengths in inches of a sample of cockroaches, you
could use
A)
a stemplot.
D)
Either (A) or (B).
B)
a pie chart.
E)
Any of (A), (B), or
(C).
C)
a scatterplot.
12. Which of these is not true of the mean of the lengths in inches of a sample of
cockroaches?
A)
must take a value greater than 0.
B)
is measured in inches.
C)
would not change if we measured these trout
in centimeters instead of inches.
D)
Both (B) and (C).
E)
Both (A) and (C).
13. Which of these is not true of the standard deviation s of the lengths in inches of a sample
of cockroaches?
A)
s must take a value between –1 and 1.
B)
s is measured in inches.
C)
s would not change if we measured these trout
in centimeters instead of inches.
D)
Both (B) and (C).
E)
Both (A) and (C).
14. Which of these is not true of the correlation r between the lengths in inches and weights
in ounces of a sample of cockroaches?
A)
r must take a value between –1 and 1.
B)
r is measured in inches.
C)
If longer trout tend to also be heavier, than r >0
.
D)
r would not change if we measured these trout
in centimeters instead of inches.
E)
Both (B) and (D).
15. A correlation cannot have the value
A) 0.4. B) –0.75. C) 1.5. D) 0.0.
E) 0.99.
16. Which correlation indicates a strong positive straight-line relationship?
A) 0.4 B) –0.75 C) 1.5 D) 0.0 E) 0.99
17. A study found that SAT Verbal scores were positively associated with first-year grade
A)
B)
C)
D)
E)
point averages for liberal arts majors. We can conclude from this that
students who scored high on the SAT Verbal
test tended to get lower GPAs than those who
scored lower on the SAT Verbal test.
students who scored high on the SAT Verbal
test tended to get higher GPAs than those who
scored lower on the SAT Verbal test.
we can use the SAT verbal score to accurately
predict GPAs for liberal arts majors.
grade point averages are higher for older
students.
the correlation between the SAT Verbal score
and GPA is higher than 0.5.
18. You calculate the correlation between height and weight for a simple random sample of
50 students from your college. Another student does the same for a simple random
sample of 200 students from the college. The other student should get
A)
a correlation greater than 1.
B)
a correlation less than –1.
C)
a higher value for the correlation.
D)
a lower value for the correlation.
E)
about the same value for the correlation.
19. In a scatterplot we can see
A)
B)
C)
D)
E)
a display of the five-number summary.
whether or not we have a simple random
sample.
the shape, center, and spread of the distribution
of a quantitative variable.
the form, direction, and strength of a
relationship between two quantitative
variables.
Kansas.
20. The correlation between two variables is of –0.8. We can conclude
A)
one causes the other.
B)
there is a strong positive association between
the two variables.
C)
there is a strong negative association between
the two variables.
D)
all of the relationship between the two
variables can be explained by a straight line.
there are no outliers.
E)
21. The heights of a random sample of students in this class were recorded in inches. They
were then converted to the metric scale using the fact that one inch is the same as 2.54
centimeters. What is the correlation between the heights in inches and the heights in
centimeters?
A)
Cannot be determined from the information
given.
B)
2.54
C)
0.5
D)
1.0
E)
–1.0
The following two questions are related to questions 19-21 in Chapter 15.
Use the following to answer questions 22-23:
The correlation between the heights of fathers and the heights of their (adult) sons is
r = 0.52.
22. This tells us that
A)
B)
C)
D)
E)
taller than average fathers tend to have taller
than average sons.
taller than average fathers tend to have shorter
than average sons.
sons are, on the average, taller than their
fathers.
52% of all sons are taller than their fathers.
there is almost no connection between heights
of fathers and sons.
23. If fathers' heights were measured in feet (one foot equals 12 inches), and sons' heights
were measured in furlongs (one furlong equals 7,920 inches), the correlation between
heights of fathers and heights of sons would be
A)
much smaller that
D)
slightly larger than
0.52.
0.52.
B)
slightly smaller than
E)
much larger that 0.52.
0.52.
C)
unchanged: equal to
0.52.
24. If two variables, x and y, each have standard deviation one, and if the average of the
products (x – )(y – ) is –0.25, then the correlation between the variables is
A) +1. B) positive. C) zero. D) –0.25. E) –1.
25. To display the relationship between per capita wine consumption and heart disease death
rates per 100,000 people in each of 29 countries, a good choice of a graph would be an
A) angiogram. B) boxplot. C) histogram. D) line graph. E) scatterplot.
A)
B)
C)
26. Which of the values below is impossible for the descriptive measure in question?
r = 1.25
D)
Both (A) and (B).
= –0.2
E)
Both (A) and (C).
s = 3.4
27. A study of new cars finds that the correlation between the weight of cars (pounds) and
their city gas mileage (miles per gallon) is r = –0.4. This tells us that
A)
heavier cars tend to get more miles per gallon.
B)
heavier cars tend to get fewer miles per gallon.
C)
there is almost no connection between weight
and gas mileage.
D)
an arithmetic error was made because the
correlation must be greater than 0.
E)
the mean gas mileage has gone down since last
year.
28. You would draw a scatterplot
A)
B)
C)
D)
E)
to show the distribution of heights of students
in this course.
to compare the distributions of heights for
male and female students in this course.
to show how a child's height increases over
time.
to show the five-number summary for the
heights of female students.
to show the relationship between the heights of
female students and the heights of their
mothers.
29. A student doing a science fair project tries to germinate tomato seeds at different soil
temperatures. She writes, "I planted 10 seeds at each of three temperatures. I found that
20% germinated at 55, 40% germinated at 60, and 37% germinated at 65." Why must
her report be wrong?
A)
37% is not a possible percent in this situation.
B)
The three percents given don't add to 100%.
C)
It's wrong to report percents; she should report
the correlation r.
D)
This isn't a randomized comparative
experiment.
E)
It isn't possible for fewer seeds to germinate at
60 than at 65.
30. A study of the effects of television measured how many hours of television each of 125
grade school children watched per week during a school year and their reading scores.
Which variable would you put on the horizontal axis of a scatterplot of the data?
A)
Reading score, because it is the response
variable.
B)
Reading score, because it is the explanatory
variable.
C)
Hours of television, because it is the response
variable.
D)
Hours of television, because it is the
explanatory variable.
E)
It makes no difference, because there is no
explanatory-response distinction in this study.
The following two questions are related to questions 37-39 in Chapter 12.
Use the following to answer questions 31-32:
Here are the survival times (in days) of 50 guinea pigs that were injected with a bacterial
infection in a medical study.
43 45 53 56 56 57 58 66 67 73
74 79 80 80 81 81 81 82 83 83
84 88 91 92 92 97 99 99 100 101
102 103 107 109 114 121 126 137 139 145
156 164 179 191 204 211 228 243 260 285
31. To display the pattern of the survival times, what type of graph would you make?
A)
a stemplot
B)
a scatterplot
C)
a line graph
D)
a pie chart
E)
Either a stemplot or a scatterplot would work
well.
32. Which of these descriptive numbers for the guinea pig data is not measured in days?
the mean survival time
the standard deviation of the survival times
the correlation between survival time and age
of the animal
D)
the median survival time
E)
Both (B) and (C).
A)
B)
C)
The following question is related to questions 33-34 in Chapter 13.
33. Scores on the American College Testing (ACT) college entrance exam follow the
normal distribution with mean 18 and standard deviation 6. Wayne's standard score on
the ACT was –1.1. Wayne tells Garth, "There is a correlation of r = 1.51 between the
gender of factory workers and their salary." Wayne's statement makes no sense because
A)
the correlation is actually negative.
B)
the correlation can't be larger than 1.
C)
gender is a categorical variable, so correlation
makes no sense.
D)
the correlation should be given in units, like
dollars.
E)
Both (B) and (C).
34. There is a strong straight-line association between the height and the arm lengths of a
group of people. Knowing this, a reasonable value for the correlation coefficient
between height and arm length is
A) r = 1. B) r = 0.8. C) r = 0. D) r = –0.8. E) r = –1.
35. You have data on the summer earnings of a sample of 1,000 college students. What
kind of graph should you use to describe the distribution of their earnings?
A) bar chart B) histogram C) line graph D) pie chart E) scatterplot
Use the following to answer questions 36-37:
A study of home heating costs collects data on the size of houses and the monthly cost to heat the
houses with natural gas. Here are the data:
Size of House
1200 sq ft
2300 sq ft
1800 sq ft
2000 sq ft
Heating Cost
$150
$375
$270
$315
36. Just by looking at the data (don't do a calculation) you can see that the correlation
between house size and heating cost is
A)
close to zero.
B)
clearly positive.
C)
clearly negative.
D)
not close to zero, but could be either positive
or negative.
E)
Makes no sense for these data.
37. A friend tells you that the correlation for the data is r = 0.99984. You conclude from
this number that
A)
larger houses cost more to heat than smaller
houses, and the relationship is almost perfectly
straight.
B)
smaller houses cost more to heat than larger
houses, and the relationship is almost perfectly
straight.
C)
larger houses cost more to heat than smaller
houses, but the relationship is not very strong.
D)
smaller houses cost more to heat than larger
houses, but the relationship is not very strong.
E)
your friend made a mistake, because the value
of r is impossible.
38. A study found correlation r = 0.43 between high school math grades (on a 0 to 100
scale) and income 10 years after high school. This means that
A)
people with high math grades tend to have
higher income than people with low math
grades.
B)
people with low math grades tend to have
higher income than people with high math
C)
D)
E)
grades.
there is almost no association between math
grades and income.
a mistake has been made, because a correlation
cannot be 0.43.
a mistake has been made, because a correlation
between math grades and income makes no
sense.
39. You catch several cockroaches in a dormitory and measure their lengths in centimeters.
Which of these sets of numerical descriptions are all measured in centimeters?
A)
median length, largest length, count of
cockroaches
B)
five-number summary of the lengths
C)
mean length, standard deviation of lengths,
median length
D)
mean length, median length, correlation
between length and weight
E)
Both (B) and (C).
40. Which of the statements does not contain a statistical blunder?
A)
There is a strong negative correlation between
a person's sex and the amount that he or she
pays for automobile insurance.
B)
The standard deviation of scores on the first
STAT 001 exam was
s = –14 points.
C)
The mean height of young women is 64 inches,
and the correlation between their heights and
weights is 0.6 inches.
D)
The correlation between height and weight for
adult females is about r = 1.2.
E)
All four statements contain blunders.
The following four questions are related to question 35 in Chapter 15.
Use the following to answer questions 41-44:
An education researcher measured the IQ test scores of 78 seventh-grade students in a rural
school, and also their school grade point average (GPA). Here is a graph of GPA versus IQ for
these students:
41. The name for this kind of graph is a
A) histogram. B) bivariate plot.
C) boxplot.
D) scatterplot.
42. The IQ score of the student who has the lowest GPA is
A) about 103. B) about 0.6. C) about 72. D) about 7.2.
43. The graph shows
A)
a clear positive
C)
association.
B)
very little association. D)
a clear negative
association.
a skewed distribution.
44. One of these numbers is the correlation r between IQ score and GPA. Which is it?
A) r = 0.02 B) r = 0.63 C) r = 0.95 D) r = –0.63 E) r = –0.95
45. The standard deviation is a measure of
A)
B)
the center of a distribution.
the variability of a distribution.
C)
D)
the association between two variables.
the standardized value of a variable.
46. You measure the length in centimeters and the weight in grams of each of a litter of
newly hatched rattlesnakes. The standard deviation of the weights is measured in
A) grams. B) centimeters. C) grams squared. D) no units—it's a pure number.
47. NFL quarterbacks earn more (on the average) than running backs, who in turn earn more
than linemen. The correlation coefficient r between a player's salary and his position
A) is positive. B) is near zero. C) is negative. D) makes no sense.
48. Which of these statistical measures can never be negative?
A)
the mean
D)
B)
the standard deviation E)
C)
Both (A) and (B).
All of (A), (B), and
(C).
the correlation
coefficient
49. Consider the following data:
x
y
A) 7.6.
B) 0.0
C) 1.0.
D) –0.6.
3
–3
6
–6
–7
7
1
–1
The correlation coefficient r is
E) –1.0.
50. All 753 students in grades 1 through 6 in an elementary school are given a math test
which was designed for third graders. The body weights of all 753 students are also
recorded. We expect to see _______________ between weight and test score.
A)
positive association
B)
little or no association
C)
negative association
D)
either positive or negative association, but it's
hard to predict which
The following question is related to questions 55-57 in Chapter 12 and 45 in Chapter 15.
51. The following data set concerns five college
students, their GPAs, and their writing SAT
scores.
Student
GPA
SAT
A) –0.32.
B) 1.2.
C) 0.4.
1
2.9
650
2
3.4
680
3.7
770
The correlation coefficient r between GPA and
SAT is
D) 0.91. E) 1.
52. Tall men tend to marry women who are taller than average, but the degree of association
between the height of a husband and the height of his wife isn't very big. The
correlation between heights of husbands and wives that best describes this situation is
A) –0.9. B) –0.3. C) close to 0. D) 0.3. E) 0.9.
53. Here are the heights of a young girl at several
ages, from a pediatrician's records:
Age in
36
months
Height in centimeters
A) –0.99.
B) –0.6.
C) +0.1.
51
86
91
The correlation between the Age and Height
variables is about
D) +0.5. E) +0.99.
54. An agricultural economist says that the correlation between corn prices and soybean
prices is r = 0.7. This means that
A)
when corn prices are above average, soybean
prices also tend to be above average.
B)
there is almost no relation between corn prices
and soybean prices.
C)
when corn prices are above average, soybean
prices tend to be below average.
D)
the economist is confused, because correlation
makes no sense in this situation.
55. An educator says that the correlation between students' grades and the type of music
(rock, jazz, classical, etc.) they prefer is r = –0.7. This means that
A)
students who prefer classical music tend to
have higher grades.
B)
there is almost no relation between grades and
tastes in music.
C)
students who prefer classical music tend to
have lower grades.
D)
the educator is confused, because correlation
makes no sense in this situation.
A)
B)
C)
D)
E)
56. The numerical value of a correlation coefficient
can be any number.
can be zero or any positive number.
can be any number between 0 and 1.
can be any number between –1 and 1.
can be any number between –1 and 1 other
than 0.
57. In a long-term study of human growth, the heights and weights of 200 children are
measured and recorded each year, starting at birth and then on each birthday until the
21st. For which of the following pairs of variables will the correlation be largest?
A)
height at birth, height D)
height at age 20,
at age 10
height at age 21
B)
height at age 10,
E)
height at age 21,
weight at age 10
weight at birth
C)
weight at age 10,
weight at age 21
58. An engineer at General Motors collects data on the weights (in pounds) and the fuel
economy (in miles per gallon) of all model year 2000 cars sold by GM. We expect the
correlation between weight and gas mileage to be
A)
clearly positive.
B)
close to zero.
C)
clearly negative.
D)
Can't tell because correlation is random.
E)
Can't tell because correlation depends on the
average fuel economy of these cars.
59. A plausible value for the correlation between heights of two children of the same parents
is
A) –0.95. B) –0.50. C) close to 0. D) +0.50. E) +0.95.
60. For the data
x 0 1 2 3 4
y 9 7 5 3 1
the correlation is
A)
exactly equal to 1.
D)
B)
C)
slightly less than 1.
about 1/2.
E)
61. Correlation is a measure of
A) center. B) spread. C) trend.
D) confounding.
slightly greater than –
1.
exactly equal to –1.
E) None of the above.
62. The heights (in inches) and weights (in pounds) of all children (grades 1 to 6) at Happy
Hollow Elementary School are measured and recorded. Within each grade, the
correlation between height (in inches) and weight (in pounds) is about 0.6. The
correlation between height (in inches) and weight (in pounds) for all children at the
school is probably
A)
about 0.6.
B)
quite a bit larger than 0.6.
C)
positive, but quite a bit smaller than 0.6.
D)
negative.
63. The correlation between height (in inches) and weight (in pounds) among first-grade
students at Happy Hollow Elementary School is exactly 0.57. If heights are converted to
centimeters and weights are converted to kilograms, what happens to the correlation
between height and weight among the first-graders? (1 inch = 2.54 cm.; 1 pound = 0.394
kg.)
A)
The correlation is still 0.57.
B)
The correlation gets bigger.
C)
The correlation gets smaller.
D)
It is not possible to tell how the correlation will
change without further information.
64. If you calculate the standard deviation of a set of numbers and get –0.31, you can
conclude that
A)
there is no straight-line D)
you made an
association.
arithmetic mistake.
B)
there is negative
E)
all of the numbers are
association.
the same.
C)
the mean must be 0.
65. The correlation between average monthly temperature x and monthly natural gas
consumption y over a period of months at Lincoln High School is –0.86. Which of the
following operations would change the value of the correlation?
A)
Measure gas consumption in cubic meters
instead of cubic feet.
B)
Remove two outliers from the data before
doing the calculation.
C)
Measure temperature in degrees Kelvin instead
of in degrees Fahrenheit.
D)
All of (A), (B), and (C) would change the
value of the correlation.
66. Which of the following statements about correlation is false?
The value of correlation coefficient is heavily
influenced by outliers.
B)
The correlation coefficient can never be larger
than 1.
C)
The correlation coefficient measures how
tightly the points in a scatterplot cluster about a
straight line.
D)
The correlation coefficient cannot be 0.
A)
67. Which of the following statements about correlation r is false?
A)
r describes how tightly the points on a
scatterplot cluster about a straight line.
B)
r can never take a value larger than 1.
C)
It makes no sense to talk about a correlation
between a student's major and her income.
D)
The value of r is heavily influenced by
outliers.
E)
r measures the proportion of the variance of
one variable that can be explained by straight
line dependence on the other variable.
68. Which of these statements is true of the correlation r?
A)
r can only take values 0 or greater than 0.
B)
r can only take values between –1 and 1,
inclusive.
C)
r describes only straight-line relationships.
D)
Both (A) and (C).
E)
Both (B) and (C).
The following three questions are related to question 52 in Chapter 15.
Use the following to answer questions 69-71:
Below is a graph of the percent of adults in each state who were obese in 1991 and the percent
who were obese in 1998:
69. This type of graph is called a
A) boxplot. B) histogram.
C) line graph.
D) scatterplot.
E) stemplot.
70. Which of these is a reasonable value of the correlation r for the data in this graph?
A) r = 0 B) r = 0.3 C) r = 0.7 D) r = 0.95 E) r = 1
71. Arizona had the lowest percent obese in 1998, 12.7%. About what percent of Arizona
adults were obese in 1991?
A) 7.8% B) 11.0% C) 12.7% D) 14.7%
72. Which correlation indicates a strong negative straight-line relationship?
A) 0.5 B) –1.5 C) –0.5 D) –0.9 E) 0.9
The following question is related to question 44 in Chapter 4 and 20-21 in Chapter 21.
73. Here are the attendance figures for the lectures in a large class:
To show the evolution of attendance during the semester, what type of graph should you
draw?
A) boxplot B) histogram C) line graph D) scatterplot E) stemplot
74. There is a strong straight-line relationship between the outdoor temperature and the
amount of energy used to heat a house. Lower temperatures require more energy to
keep the house warm. Knowing this, a reasonable value for the correlation coefficient
between temperature and home energy consumption is
A) r = 1. B) r = 0.8. C) r = 0. D) r = –0.8. E) r = –1.
75. Here is a scatterplot of the percent of games won by 11 basketball teams versus the
percent of their shots that they made:
What is the correlation between these two variables?
A) about 0.8 B) about –0.3 C) close to 0 D) about 0.3
A)
B)
C)
E) about 0.8
76. Which of the values below is impossible for the descriptive measure in question?
r = 1.25
D)
Both (A) and (B).
= –0.2
E)
Both (A) and (C).
s = 3.4
77. You measure both the calories and the amount of salt in each of 33 brands of hot dogs.
The correlation between these variables is r = 0.49. This shows that
A)
hot dogs with more calories tend to have less
salt.
B)
calories and salt in hot dogs are not related at
all.
C)
the mean amount of salt is less than the mean
number of calories.
D)
the mean amount of salt is greater than the
mean number of calories.
E)
hot dogs with more salt tend to also have more
calories.
78. You read that "the correlation between a person's sex and his or her occupation is
r = 0.32." This statement is improper because
A)
0.32 is not a possible value for a correlation.
B)
correlation can't be used to describe
association between two categorical variables.
C)
D)
the association is negative, so the correlation
must be less than zero.
the five-number summary is a better
description of these data.
79. You read that "the correlation between spending on schools (dollars per pupil) and
median score on student achievement tests is r = 0.08." This means that
A)
school districts that spend a lot have higher
scores than low-spending districts, and this
effect is quite strong.
B)
school districts that spend a lot have lower
scores than low-spending districts, and the
effect is quite strong.
C)
school districts that spend a lot have somewhat
higher scores than low-spending districts, but
the effect is weak.
D)
school districts that spend a lot have somewhat
lower scores than low-spending districts, but
the effect is weak.
80. A study found correlation r = 0.61 between the sex of a worker and his or her income.
You conclude that
A)
women earn more than men on the average.
B)
women earn less than men on the average.
C)
an arithmetic mistake was made because this is
not a possible value of r.
D)
this is nonsense because correlation makes no
sense here.
81. A study found correlation r = –0.43 between how many cigarettes a person smokes and
how overweight the person is. You conclude that
A)
people who smoke more tend to be more
overweight.
B)
people who smoke more tend to be less
overweight.
C)
an arithmetic mistake was made because this is
not a possible value of r.
D)
this is nonsense because correlation makes no
sense here.
82. A psychologist finds correlation r = –0.3 between degree of internal religious
commitment and degree of racial prejudice in a large group of people. This means that
A)
people with more religious commitment tend
to be more prejudiced.
B)
an arithmetic error has been made.
C)
people with more religious commitment tend
to be less prejudiced.
D)
there is less variation in prejudice than in
religious commitment.
Use the following to answer questions 83-84:
You gather data on the number of hours of television news broadcasts watched per week and the
grade point average of juniors majoring in journalism. You expect that TV news broadcast
watching will help explain grades.
83. In a scatterplot of your data,
A)
B)
C)
D)
hours of TV news broadcast watching should
be on the horizontal axis.
grade index should be on the horizontal axis.
it makes no difference which is horizontal.
a scatterplot is not an appropriate type of graph
for these data.
84. The plot of the data in the preceding question shows that students who watch more TV
news broadcast watching tend to have higher grade indexes. You calculate the
correlation r between hours of TV and grade point average. A plausible value is
A) r = –1. B) r = –0.4. C) r = 0. D) r = 0.4.
85. A writer says that the correlation between the family income of a high school senior and
the student's college board score is r = 0.4. This means that
A)
students from high-income families tend to
have lower scores than students from lowincome families.
B)
students from high-income families tend to
have higher scores than students from lowincome families.
C)
the writer made a mistake because 0.4 is not a
possible value of the correlation.
D)
the margin of error is 0.16.
86. Which of the following pairs of variables is most likely to show a negative correlation?
a person's income and her years of education.
a car's top speed and its gas mileage (miles per
gallon)
C)
a student's grade point average and his IQ
score.
D)
a man's height and his income.
A)
B)
87. Which of the following are most likely to be negatively correlated?
A)
the total floor space and the price of an
apartment in New York
B)
the percentage of body fat and the time it takes
to run a mile for male college students
C)
the heights and yearly earnings of 35-year-old
U.S. adults
D)
gender and yearly earnings among 35-year-old
U.S. adults
E)
the prices and the weights of all racing bicycles
sold last year in Chicago
Chapter 15
The following question is related to questions 1-4 in Chapter 12 and 1-2 in Chapter 14.
Use the following to answer question 1:
The stock market did well during the 1990s. Here are the percent total returns (change in price
plus dividends paid) for the Standard & Poor's 500 stock index:
Year
Return
1990
–3.1
1991
30.5
1992 1993
7.6 10.1
1994
1.3
1995
37.6
1996
23.0
1997 1998
33.4 28.6
1999
21.0
1. If x is the percent return on the Standard & Poor’s 500 stock index and y is the percent
return on the Nikkei 225 index (a Japanese stock index) in the same year, the leastsquares regression line for predicting y from x is y = –10.4 + 0.3x . In 2000, you thought
the Standard & Poor’s 500 stock index would have a return of 10%. Using this
regression line, you would have predicted that the return on the Nikkei 225 index would
be
A) 7.4%. B) –7.4%. C) 19.6%. D) 3.%.
The next three questions are related to questions 3-5 in Chapter 14.
Use the following to answer questions 3-5:
How well does the number of beers a student drinks predict his or her blood alcohol content?
Sixteen student volunteers at The Ohio State University drank a randomly assigned number of
cans of beer. Thirty minutes later, a police officer measured their blood alcohol content (BAC).
A scatterplot of the data appears below:
2. The least-squares regression line for predicting blood alcohol content from number of
beers is y = –0.013 + 0.018x . The slope 0.018 of this line tells us that
A)
the correlation between number of beers and
BAC is 0.018.
B)
on the average, BAC increases by 0.018 for
each additional beer a student drinks.
C)
a student who drinks no beer will still have a
BAC of 0.018.
D)
the average BAC of all the students in the
study was 0.018.
3. The least-squares regression line for predicting blood alcohol content from number of
beers is y = –0.013 + 0.018x . Using this line, you predict that the BAC of a student
who drinks 5 beers will be about
A) 0.025. B) 0.077. C) 0.09. D) 0.103.
4. You wonder whether drinking coffee before a statistics exam improves the performance
of students on the exam. The best way to get good evidence of the effect of coffee on
exam scores is
A)
find out which students drink coffee before the
exam and which do not; compare their exam
scores.
B)
take an opinion poll, asking students if they
think coffee helps them stay alert.
C)
get your friends to drink coffee before Exam 1
but not before Exam 2; compare their scores on
the two exams.
D)
assign some students, chosen at random, to
drink coffee and others to avoid coffee before
the exam; compare their exam scores.
5. Consider a large number of countries around the world. There is a positive correlation
between the number of Nintendo games per person x and the average life expectancy y.
Does this mean that we could increase the life expectancy in Rwanda by shipping
Nintendo games to that country?
A)
Yes: the correlation says that as the number of
Nintendo games per person goes up, so does
life expectancy.
B)
No: if the correlation were negative we could
accept that conclusion, but this correlation is
positive.
C)
Yes: positive correlation means that if we
increase x, then y will also increase.
D)
No: the positive correlation just shows that
richer countries have both more Nintendo
games per person and higher life expectancies.
E)
It makes no sense to calculate correlation
between these variables.
6. Suppose that the correlation between the scores of students on Exam 1 and Exam 2 in a
statistics class is r = 0.7 . One way to interpret r is to say what percent of the variation
in Exam 2 scores can be explained by the straight-line relationship between Exam 2
scores and Exam 1 scores. This percent is about
A) 84%. B) 70%. C) 49%. D) 30%.
7. What can we say about the relationship between a correlation r and the slope b of the
A)
B)
C)
D)
least-squares line for the same set of data?
r is always larger than b.
r and b always have the same sign (+ or –).
b is always larger than r.
b and r are measured in the same units.
8. A "regression line" is not just any line drawn through the points of a scatterplot. What is
special about a regression line?
A)
It passes through all the points.
B)
It always uses the least-squares idea.
C)
It has slope equal to the correlation between
the two variables.
D)
It describes how a response variable y changes
as an explanatory variable x takes different
values.
The following two questions are related to question 2 in Chapter 11, 12-13 in Chapter 12, and 89 in Chapter 14.
Use the following to answer questions 9-10:
Here is a stemplot of the percent of males, 15 and older, who are illiterate in 139 countries,
according to the United Nations. For example, the highest illiteracy rate was 69%, in the African
country of Mali:
0 000000000000000011111111111122222233333334444444
0 5555666666666777777899
1 0000000111111244
1 6667788999
2 0000011123333
2 56899
3 011133
3 5789
4 0013
4 77
5 00
5 6779
6 3
6 9
9. The least-squares regression line for predicting the percent of a country's females who
are illiterate from the percent of males who are illiterate is female % = 2.32 + 1.41 
male %. In China, 4% of men are illiterate. Predict the percent of illiterate women in
China.
A) 3.7% B) 2.4% C) 8% D) 5.6%
10. The equation of the regression line tells us that (on the average) when the male illiteracy
rate goes up by 1%, the female rate goes up by
A) 3.73%. B) 2.32%. C) 1.41%. D) 0.81%.
11. There is a close relationship between the correlation r and the slope b of the leastsquares regression line. In particular, it is true that
A)
r and b always have the same sign, which
shows whether the variables are positively or
negatively associated.
B)
r and b both always take values between –1
and 1.
C)
the slope b is always at least as large as the
correlation r.
D)
the slope b is always equal to r2, the square of
the correlation.
E)
Both (A) and (B) are true.
12. The Current Population Survey records the incomes of a large sample of American
households. To briefly describe the distribution of household income, it is best to use
A)
the mean and standard C)
the five-number
deviation.
summary.
B)
the mean and the
D)
a regression line.
median.
13. We want to use scores on Exam 1 to predict final total score in a course. Last semester,
students with higher Exam 1 scores did tend to get higher total scores. But regressing
total score on Exam 1 score explained only 36% of the total score. What is the
correlation between Exam 1 scores and total scores?
A) 0.36 B) –0.36 C) 0.60 D) –0.60 E) 0.72
14. A study of 3,617 adults found that those who attend religious services live longer (on the
average) than those who don't. Is this good evidence that attending services causes
longer life?
A)
B)
C)
D)
Yes, because the study is an experiment.
No, because religious people may differ from
non-religious people in other ways, such as
smoking and drinking, that affect life span.
Yes, because the sample is so large that the
margin of error will be quite small.
No, because we can't generalize from 3,617
people to the millions of adults in the country.
15. The correlation between two variables x and y is 0.5. If we used a regression line to
predict y using x, what percent of the variation in y would be explained?
A) 50% B) 25% C) 2.23% D) 75% E) 0%
16. If the least-squares regression line for predicting y from x is y = 500 – 20x, what is the
predicted value of y when x = 10 ?
A) 300 B) 500 C) 200 D) 700 E) 20
17. Suppose that the least-squares regression line for predicting y from x is y = 100 + 1.3x.
Which of the following is a possible value for the correlation between y and x?
A) 1.3 B) –1.3 C) 0 D) –0.5 E) 0.5
18. A report in a medical journal notes that the risk of developing Alzheimer's disease
among subjects who (voluntarily) regularly took the anti-inflammatory drug ibuprofen
(the active ingredient in Advil) was about half the risk among those who did not. Is this
good evidence that ibuprofen is effective in preventing Alzheimer's disease?
A)
Yes, because the study was a randomized,
comparative experiment.
B)
No, because the effect of ibuprofen is
confounded with the placebo effect.
C)
Yes, because the results were published in a
reputable professional journal.
D)
No, because this is an observational study. A
clinical trial would be needed to confirm (or
not confirm) the observed effect.
E)
Yes, because a 50% reduction can't happen just
by chance.
The following three questions are related to questions 22-23 in Chapter 14.
Use the following to answer questions 19-21:
The correlation between the heights of fathers and the heights of their (adult) sons is
r = 0.52 .
19. The correlation r = 0.52 shows that the fact that fathers have different heights
A)
explains about 27% of the observed variation
in their sons' heights.
B)
explains about 52% of the observed variation
in their sons' heights.
C)
explains about 73% of the observed variation
in their sons' heights.
D)
explains about 95% of the observed variation
in their sons' heights.
E)
explains why some sons look up to their
fathers more than others.
20. The equation of the regression line for son's height in inches y versus father's height in
inches x is y = 0.5x + 35. For 72-inch-tall fathers, what is the mean height of their sons?
A)
69 inches
D)
74 inches
B)
71 inches
E)
None of the above.
C)
72 inches
21. Not only is the correlation between the heights of fathers and the heights of their (adult)
sons close to one half, but also the standard deviations of fathers' heights and of sons'
heights are just about the same. This tells us that
A)
among fathers who are two inches above
average in height, their sons are, on the
average, only one inch above average in
height.
B)
among sons who are two inches above average
in height, their fathers are, on the average, only
one inch above average in height.
C)
among sons who are two inches above average
in height, their fathers are, on the average, four
inches above average in height.
D)
Both (A) and (B) are true.
E)
Both (A) and (C) are true.
22. Perfect correlation means all of the following except
A)
r = –1 or r = +1.
B)
all points on the scatterplot lie on a straight
line.
C)
all variation in one variable is explained by
variation in the other variable.
D)
there is a causal relationship between the
variables.
E)
each variable is a perfect predictor of the other.
23. If there were something genetic which made people simultaneously more susceptible to
both smoking and lung cancer, that would be an instance of
A)
causation.
D)
the placebo effect.
B)
common response.
E)
voluntary response.
C)
confounding.
24. A study of new cars finds that the correlation between the weight of cars (pounds) and
their city gas mileage (miles per gallon) is r = –0.4. The correlation r = –0.4 shows that
A)
16% of the observed variation in their gas
mileages is explained by a straight-line
relationship between weight of cars and their
gas mileage.
B)
20% of the observed variation in their gas
mileages is explained by a straight-line
relationship between weight of cars and their
gas mileage.
C)
40% of the observed variation in their gas
mileages is explained by a straight-line
relationship between weight of cars and their
gas mileage.
D)
60% of the observed variation in their gas
mileages is explained by a straight-line
relationship between weight of cars and their
gas mileage.
E)
80% of the observed variation in their gas
mileages is explained by a straight-line
relationship between weight of cars and their
gas mileage.
25. A high correlation between two variables does not always mean that changes in one
cause changes in the other. The best way to get good evidence that cause-and-effect is
present is to
A)
B)
C)
D)
E)
select a simple random sample from the
population of interest.
arrange the data in a two-way table.
carry out a randomized comparative
experiment.
make a scatterplot and look for a strong
association.
make a histogram and look for outliers.
26. A study of the effects of television measured how many hours of television each of 125
grade school children watched per week during a school year and their reading scores.
The study found that children who watch more television tend to have lower reading
scores than children who watch fewer hours of television. The study report says that
"Hours of television watched explained 9% of the observed variation in the reading
scores of the 125 subjects." The correlation between hours of TV and reading score must
be
A)
r = 0.09.
D)
r = –0.3.
B)
r = –0.09.
E)
Can't tell from the
information given.
C)
r = 0.3.
27. A study of child development measures the age (in months) at which a child begins to
talk and also the child's score on an ability test given several years later. The study asks
whether the age at which a child talks helps predict the later test score. The leastsquares regression line of test score y on age x is y = 110 – 1.3x. According to this
regression line, what happens (on the average) when a child starts talking one month
later?
A)
The test score goes down 110 points.
B)
The test score goes down 1.3 points.
C)
The test score goes up 110 points.
D)
The test score goes up 1.3 points.
E)
The test score is 108.7.
28. A study showed that students who study more hours tend to do better on statistics
exams. In fact, number of hours studied explained 81% of the variation in exam scores
among the students who participated in the study. What is the correlation between hours
studied and exam score?
A) r = 0.9 B) r = 0.81 C) r = 0.656 D) r = –0.656 E) r = –0.9
29. Deaths from highway accidents went down after the adoption of a national 55 mile-perhour speed limit. Can we be confident that the lower speed limit caused the drop in
deaths?
A)
Yes, because the study was a randomized,
comparative experiment.
B)
No, because the effect of lower speed limits is
confounded with the effect of better highways
and safer cars.
C)
Yes, because a drop in deaths over several
years can't happen just by chance.
D)
No, because of the placebo effect.
E)
Yes, because correlation implies causation.
30. Once you have decided to use the median to describe the center of a distribution of data,
it makes sense to describe the spread by
A)
the two quartiles.
D)
the correlation.
B)
the standard deviation. E)
the least-squares
regression line.
C)
the mean.
Use the following to answer questions 31-34:
A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the
amount of natural gas a household consumes, in cubic feet per day. Call the temperature x and
gas consumption y. The house is heated with gas, so x helps explain y. The least-squares
regression line for predicting y from x is y = 1360 – 20x.
31. On a day when the temperature is 20F, the regression line predicts that gas used will be
about
A)
17,604 cubic feet.
D)
960 cubic feet.
B)
1,360 cubic feet.
E)
None of these.
C)
1,160 cubic feet.
32. We can see from the equation of the line that
A)
as the temperature x goes up, gas used y goes
up, because the slope 1,360 is positive.
B)
as the temperature x goes up, gas used y goes
up, because the slope 20 is positive.
C)
as the temperature x goes up, gas used y goes
down because the slope 1,360 is bigger than
19.
D)
as the temperature x goes up, gas used y goes
down, because the slope –20 is negative.
33. When the temperature goes up 1, what happens to the gas usage predicted by the
regression line?
A)
It goes up 1 cubic foot. D)
It goes down 20 cubic
feet.
B)
It goes down 1 cubic E)
Can't tell without
foot.
seeing the data.
C)
It goes up 20 cubic
feet.
34. The correlation between temperature x and gas usage y is r = –0.7. Which of the
following would not change r?
A)
measuring temperature in degrees Celsius
instead of degrees Fahrenheit
B)
removing two outliers from the data used to
calculate r
C)
measuring gas usage in hundreds of cubic feet,
so that all values of y are divided by 100
D)
Both (A) and (C).
E)
All of (A), (B), and (C).
The following question is related to questions 41-44 in Chapter 14.
35. A education researcher measured the IQ test scores of 78 seventh-grade students in a
rural school, and also their school grade point average (GPA). Here is a graph of GPA
versus IQ for these students:
The line drawn on the graph is the least-squares regression line of GPA on IQ. Use this
line to predict the GPA of a student with IQ 110. Your prediction is
A) GPA about 1.7. B) GPA about 6. C) GPA about 7.5. D) GPA about 9.
36. There is a positive correlation between the size of a hospital (measured by number of
beds) and the median number of days that patients remain in the hospital. Does this
mean that you can shorten a hospital stay by choosing to go to a small hospital?
A)
No—a negative correlation would allow that
conclusion, but this correlation is positive.
B)
Yes—the data show that stays are shorter in
smaller hospitals.
C)
No—the positive correlation is probably
explained by the fact that seriously ill people
go to large hospitals.
D)
Yes—the correlation can't just be an accident.
37. Students with above average scores on Exam 1 in STAT 001 tend to also get above
average scores on Exam 2. But the relationship is only moderately strong. In fact, a
linear relationship between Exam 2 scores and Exam 1 scores explains only 36% of the
variance of the Exam 2 scores.
A)
The correlation between Exam 1 scores and
Exam 2 scores is r = 0.36.
B)
The correlation between Exam 1 scores and
Exam 2 scores is r = 0.6.
C)
The correlation between Exam 1 scores and
Exam 2 scores is either 0.36 or –0.36 (can't tell
which).
D)
The correlation between Exam 1 scores and
Exam 2 scores is either 0.6 or –0.6 (can't tell
which).
There is not enough information to say what r
is.
E)
38. Martin would like to show that drinking one beer before a STAT 001 exam improves
students' exam scores. The most convincing way to show this is
A)
ask all STAT 001 students whether or not they
drank a beer before the exam, then compare
the mean scores of those who did and those
who did not.
B)
ask all STAT 001 students if they think that
drinking a beer helps them on exams.
C)
interview 50 students who got an A on the
exam and 50 students who got a D and
compare their beer drinking.
D)
randomly choose 50 students to drink beer
before the exam and another 50 to abstain from
beer. Compare the mean exam scores in the
two groups.
39. A psychologist is interested in the effects of religious conversion on alcoholics. She
locates 50 alcoholics who have recently joined evangelical churches, and matches each
with another alcoholic of the same age, occupation, and family status who has not joined
a church. All 100 subjects are then observed for 5 years. This is
A)
a randomized comparative experiment.
B)
an experiment, but without randomization.
C)
a sample survey with randomly selected
respondents.
D)
a comparative observational study.
Use the following to answer questions 40-44:
Scores x on the SAT Writing among Kentucky high school seniors in a recent year were normally
distributed with mean 550 and standard deviation 100. The scores y of the same students on the
SAT Math were normally distributed with mean 570 and standard deviation 100. The leastsquares regression line for predicting math score from writing score has the equation y = 0.6x +
240
40. The correlation between writing scores and math scores is
A) 0.6.
B) –0.6.
C) 0.
D) Can't be determined.
41. For those students who scored 500 on the writing l test, the mean score on the
mathematics test was
A) 520. B) 540. C) 570. D) Can't be determined.
42. Joe's writing test score was 450 (1 standard deviation below the population mean 550).
A good guess for Joe's mathematics test score is
A) 510. B) 490. C) 470. D) 270.
43. Among those students whose writing test scores were at about the 30th percentile, most
probably had mathematics test scores that were
A)
above the population C)
below the 30th
median.
percentile.
B)
at about the 30th
D)
above the 30th
percentile.
percentile.
44. About what percent of all students taking the exam were above average on both the
writing section and the mathematics section?
A) more than 50% B) about 50% C) more than 25% D) less than 25%
The following question is related to questions 55-57 in Chapter 12 and 51 in Chapter 14.
45. The following data set concerns five college
students, their GPAs, and their Writing SAT
scores:
Student
GPA
SAT
A) 3.72.
B) 3.79.
C) 3.70.
1
2.9
650
2
3.4
680
3.7
770
Suppose we wanted to predict the future GPA
of a sixth incoming student who has an SAT
score of 788. Our best prediction on the basis
of the given data would be
D) 3.75. E) 3.85.
46. From past data on students at Mountain State College, we find the following leastsquares regression line for predicting a student's college GPA y from the student's
entrance SAT (Critical Reading + Writing + Math) score x: y = 0.3 + 0.0022x. A
prospective student applying for admission to Mountain State has combined (Critical
Reading + Writing + Math) SAT score 2,250. What is your best prediction of this
student's GPA at Mountain State if he/she were admitted?
A)
about 6.0
D)
about 5.0
B)
about 5.8
E)
less than 5.0
C)
about 5.3
47. A study of many countries finds a strong positive correlation between the life
expectancy in a country and the percentage of households in the country with
telephones. This means that
A)
telephone use is a major contributing cause of
longer life.
B)
life expectancy could be significantly
increased by installing more telephones.
C)
in countries where life expectancy is high,
telephone ownership tends to be low.
D)
in countries where telephone ownership is low,
life expectancy tends to be high.
E)
None of the above.
48. You compute the correlation coefficient between hours of TV watched and grade point
average for a sample of college undergraduates and obtain r = –1.83. This means that
A)
you made an arithmetic mistake.
B)
students who watch more TV tend to get lower
grades.
C)
students who watch more TV tend to get
higher grades.
D)
you can conclude that radiation from TV
screens causes gradual brain damage.
E)
you can conclude that students who get good
grades gradually lose their ability to appreciate
TV.
49. The best way to settle questions of causation is
A)
a careful observational D)
study.
draw a line graph.
B)
C)
a properly designed
experiment.
draw a scatterplot.
E)
calculate a correlation.
Use the following to answer questions 50-51:
Lean body mass (your weight leaving out fat) helps predict metabolic rate (how many calories of
energy you burn in an hour). The relationship is roughly a straight line. The least-squares
regression line for predicting metabolic rate (y in calories) from lean body mass (x in kilograms)
is y = 113.2 + 26.9x.
50. Using this regression line, you predict that a person with lean body mass 50 kilograms
will have metabolic rate equal to about how many calories?
A) 140 B) 1,232 C) 1,345 D) 1,458 E) 5,687
51. The slope of the regression line is
A)
B)
C)
D)
E)
113.2—that is, when x = 0, y = 113.2.
113.2—that is, the mean metabolic rate is
113.2 calories per hour.
26.9—that is, the mean metabolic rate is 26.9
calories per hour.
26.9—that is, when lean body mass goes up by
1 kg, metabolic rate goes up by 26.9 calories.
26.9—that is, when a person weighs 26.9 more
kg, metabolic rate goes up by 1 calorie.
The following question is related to questions 69-71 in Chapter 14.
52. Below is a graph of the percent of adults in each state who were obese in 1991 and the
percent who were obese in 1998:
The least-squares regression line for predicting 1998 percent obese from 1991 percent
obese is y = 7.4 + 0.86x. In 1991, 14.8% of Indiana adults were obese. Based on this
information, what percent would you predict to be obese in 1998?
A) 5.3% B) 7.5% C) 12.7% D) 19.5% E) 20.1%
53. Investment advisors now often report correlations. For example, the correlation
between gains and losses in large cap stocks and gains and losses in municipal bonds is
r = 0.45 . This means that the percent of changes in municipal bond performance that
can be explained by the straight line relationship between municipal bonds and large cap
stocks is
A) 90%. B) 67%. C) 45%. D) 20%.
54. If the least-squares regression line for predicting y from x is y = 40 + 10x, what is the
predicted value of y when x = 5 ?
A) 90 B) 50 C) 40 D) 10 E) 140
55. The correlation between two variables x and y is –0.6. If we used a regression line to
predict y using x, what percent of the variation in y would be explained?
A) 20% B) 36% C) –36% D) 6% E) –6%
56. A high correlation between two variables does not always mean that changes in one
causes changes in the other. The best way to get good evidence that cause-and-effect is
present is to
A)
B)
C)
D)
E)
make side-by-side boxplots.
carry out a randomized comparative
experiment.
make a histogram and look for outliers.
make a scatterplot and look for a strong
association.
select a simple random sample from the
population of interest.
57. Which of the following statements about correlation is false?
The correlation coefficient measures how
tightly the points on a scatterplot cluster about
a straight line.
B)
It is impossible to get a correlation greater than
1.
C)
Correlation makes no sense for categorical
variables.
D)
The correlation coefficient is the proportion of
the variance of one variable that can be
explained by straight-line dependence on the
other variable.
E)
The correlation coefficient is heavily
influenced by outliers.
A)
58. The label on a package of hot dogs tells you how much salt each hot dog has. You want
to use this information to predict how many calories the hot dog has. The correlation is
r = 0.49. This says that
A)
the fact that hot dogs have different amounts of
salt explains about 24% of the observed
variation in their calorie counts.
B)
the fact that hot dogs have different amounts of
salt explains about 49% of the observed
variation in their calorie counts.
C)
the fact that hot dogs have different amounts of
salt explains about 70% of the observed
variation in their calorie counts.
D)
the fact that hot dogs have different amounts of
salt explains about 98% of the observed
variation in their calorie counts.
59. Grades in STAT 001 are based on total points out of 500 possible; the final exam
contributes 100 of the 500 points. Students with higher totals out of the 400 points
before the final tend to do better on the final than students with lower pre-final totals. In
fact, the linear relationship between pre-final total and final exam score explains about
half of the variation seen in the class's final exam scores.
A)
The correlation between pre-exam total and
final exam score is about r = 0 .5.
B)
The correlation between pre-exam total and
final exam score is about r = –0.5.
C)
The correlation between pre-exam total and
final exam score is about r = 0.7.
D)
The correlation between pre-exam total and
final exam score is about r = –0.7.
E)
There is not enough information to say what
the correlation is.
60. The evidence that smoking causes lung cancer is very strong. But it is not the strongest
possible statistical evidence because
A)
we can't do experiments to compare smokers
and non-smokers.
B)
only smokers have been studied.
C)
the studies of the effects of smoking are not
double-blind.
D)
all the studies of the effects of smoking involve
animals, not humans.
61. Students who study German in high school tend to score higher on tests of English
grammar than students who do not study German. Which is true?
A)
This shows that studying German improves
your knowledge of English grammar.
B)
Students who choose to study German are
probably already good at grammar, so we can't
conclude anything about cause-and-effect.
C)
This makes no sense because you can't
compute the correlation between studying
German and English grammar test scores.
D)
There is a positive correlation between whether
or not a student studied German and the
student's English grammar test score.
Chapter 16
1. Some people buy the stock of small companies. The Russell 2000 index, which tracks
the price of such shares, was 510 on December 31, 1999. On December 31, 2007, the
index was 772. What percent decrease is this?
A) 151.4% B) 66.0% C) 33.96% D) 51.4%
2. A pair of soccer shoes cost $50.00 in 1998; a pair of the same type of shoes costs
$120.00 in 2008. Using 1998 as the base year, what is the soccer shoe index number for
2008?
A) $120.00 B) $50.00 C) 240 D) 41.7 E) 2.4
3. The runner's fixed market basket consists of one pair of shoes and five pairs of socks. In
1998 the shoes cost $35.00 and the socks cost $1.00 per pair. In 2008 the shoes cost
$65.00 and the socks cost $3.00 per pair. What is the runner's fixed market basket price
index in 2000 using 1995 as the base year?
A) $40.00 B) $80.00 C) 200 D) 50 E) 186
4. Tuition at Purdue University for residents of Indiana was $7,317 for the 2008–2009
academic year. The CPI for September 2008 was 218.8 and the CPI for 1990 was 130.7.
What is the 2008–2008 tuition in 1990 dollars?
A) $218.80 B) $4,371 C) $12,249 D) $130.70 E) $1,674
5. An ad from a local appliance store says, "Double the Difference Price Protection: If,
during the first 30 days from the date you purchase a product from H. H. Gregg, you
find the same item at a lower price at another store we will refund 200% of the
difference." What does this mean?
A)
It means that H. H. Gregg will reduce its price
by 200%.
B)
It means that H. H. Gregg will reduce its price
to one-third of what it was.
C)
It makes perfectly good sense, as long as the
other store's price is at least half of H. H.
Gregg's price.
D)
It's nonsense, because refunding 100% of the
difference already reduces the cost to zero.
E)
It's nonsense because percents only make sense
for counts, and the price of an appliance isn't a
count.
6. The average price of a pound of sliced bacon was $3.40 in June 2007 and $4.00 in June
2008. What is the sliced bacon index number (June 2007 = 100) for June 2008?
A) 18 B) 60 C) 85 D) 117.6 E) 400
7. The September 2008 CPI was 218.8. The CPI component for educational books and
supplies was 459. This means that
A)
educational books and supplies costs rose
459% while overall prices rose only 218.8%.
B)
educational books and supplies costs rose
359% while overall prices rose only 118.8%.
C)
the average educational books and supplies
cost was more than four times as high in 2008
as it was in the 1982 to 1984 period, while,
overall, prices were only about 2.2 times as
high.
D)
Both (A) and (C) are true.
E)
Both (B) and (C) are true.
8. The September 2008 CPI (1982–84 = 100) was 218.8 but the component of the CPI for
personal computers was 92.9. There were great improvements in quality and features in
personal computers between 1982–1984 and 2008. We can say that
A)
the actual average price of a personal computer
in 2008 was only 92.9% of the average price in
1982–1984.
B)
the actual average price of a personal computer
in 2008 was 218.8% of the average price in
1982–1984.
C)
if a personal computer sold for $1000 in 1982–
1984, that same computer would sell for only
$929 in 2008.
D)
Both (A) and (C) are true.
9. In 2008, consumers tended to buy bigger-screen TV sets than they did in the 1982–1984
base period. How does the CPI reflect this fact?
A)
It doesn't, because it uses a fixed market
basket.
B)
It can't possibly, because if it did, the price of
C)
D)
E)
TVs would have gone up instead of down.
Every month there is a new Consumer
Expenditure Survey, which records what
consumers actually buy, so the market basket
changes every month.
The Bureau of Labor Statistics (BLS) adjusts
the actual price to subtract out the part that
pays for improved quality.
The BLS corrects by using a different base
period.
10. In addition to the national CPIs, the BLS publishes separate CPIs for 29 large
metropolitan areas. These local CPIs are considerably less precise (that is, they have
considerably more sampling variation). This is because
A)
of variation in prices among these metropolitan
areas.
B)
the monthly CPI sample size within each
metropolitan area is much smaller than the
national sample size.
C)
the monthly CPI sample sizes within the
metropolitan areas are not proportional to their
population sizes.
D)
the metropolitan areas are not randomly
selected.
E)
of variation in weather conditions among these
metropolitan areas.
11. You have data on the summer earnings of a sample of 1,000 college students. What
numerical summary should you use to describe the earnings data?
A)
Consumer Price Index D)
least-squares
regression line
B)
correlation coefficient E)
standard score
C)
five-number summary
12. Having taken statistics, you know that a graph that shows how the cost of attending your
school has increased since 1980 should show the cost in real terms. To do this, you will
A)
report cost on the standard (z) scale.
B)
use the CPI to adjust each year's cost for
changes in the buying power of a dollar.
C)
be sure to put cost on the horizontal axis of
your graph.
D)
E)
be sure to put cost on the vertical axis of your
graph.
use the median cost rather than the mean cost.
13. If the Consumer Price Index (1982–84 = 100) is 218.8, this means that
A)
prices have increased 218.8%, so that it now
costs $218.80 to buy goods and services that
cost $100 in 1984.
B)
prices have increased 218.8%, so that it now
costs $318.80 to buy goods and services that
cost $100 in 1984.
C)
taking 1984 = 100, the current price is
1984/218.8 = $9.07.
D)
a mistake has been made, because 1984 is
greater than 100.
E)
a mistake has been made, because an index
number can only take values between 0 and
100.
14. Athletes make more now, but prices are also higher than in the past. In 2003, the
basketball player Lebron James signed a contract for $90 million with Nike. How much
is this in 1975 dollars? (The CPI was 53.8 in 1975 and was 184 in 2003.)
A)
about $308 million
D)
about $26 million
B)
about $37 million
E)
about $16 million
C)
about $90 million
15. Most economists agree that the Consumer Price Index slightly overstates the rate of
inflation (the decline in the dollar's buying power). The main reason is
A)
the CPI is not based on a randomized
comparative experiment.
B)
the CPI uses 1982-1984 = 100, and this has
become out of date.
C)
the CPI market basket is just a guess at what
people really buy; it should be replaced by a
random sample of goods and services.
D)
the CPI doesn't use a standard score, so
changes in the standard deviation affect the
value of the CPI.
E)
the fixed market basket doesn't adjust quickly
enough for new products and improvements in
quality.
16. When Julie entered college in 2003, she dreamed of making $50,000 when she
graduated. The CPI in 2003 was 184. Julie graduated in 2008. (Thinking about money
rather than studies slowed her progress a bit.) The June 2008 CPI was 218.8. What must
Julie earn in order to have the same buying power that $50,000 had in 2003?
A)
about $109,400
D)
about $42,000
B)
about $92,000
E)
Can't say from the
information given.
C)
about $59,500
17. A gallon of unleaded gasoline cost $1.19 in 1980 and $4.05 in July 2008. The gasoline
price index number (1980 = 100) for July 2008 is
A)
(4.05/1.19) 100 = 340.3 .
B)
(1.19/4.05)  100 = 29.4.
C)
(4.05 – 1.19)  100 = 286.
D)
((4.05 – 1.19)/(2008 – 1980)) = 0.102.
18. When Fidel Castro was a child, he wrote a letter to President Franklin Roosevelt, asking
Roosevelt to send him a five-dollar bill. (I'm not making this up.) If Castro sent his
letter in 1940, how much was he asking for in 2007 dollars? (The CPI in 2007 was about
15 times what it was in 1940.)
A) $5 B) $75 C) $0.5 D) $7.50 E) None of these.
19. To graphically show how the Consumer Price Index has changed over the last 50 years,
one should draw
A)
a bar graph with horizontal bars of equal
widths.
B)
a pie chart.
C)
a line graph with time on the vertical axis.
D)
a line graph with time on the horizontal axis
E)
a scatterplot.
20. The most recent value of the Consumer Price Index (1982-84 = 100) is 218.8. This
means that
A)
household income has increased by 118.8%
since 1982-1984.
B)
1999 is 165% of 1982.
C)
for every $100 the government printed in
D)
E)
1982-1984, it prints $218.80 now.
consumers now spend $218.80 for every $100
they spent in 1982-1984.
a market basket of goods and services that cost
$100 in 1982 to 1984 now costs $218.80.
21. The Consumer Price Index (CPI) somewhat overstates the rise in prices over time. One
reason for this is
A)
the government uses voluntary response
samples to gather price information.
B)
many products improve in quality over time, so
higher prices are partly paying for better
quality.
C)
the CPI market basket never changes, so it has
out-of-date products such as typewriters.
D)
the government uses small samples, so there is
a lot of sampling variability in the CPI.
E)
prices are recorded in only a few places, and
some of these are places where prices are
higher than in Indiana.
22. The Consumer Price Index (1982-84 = 100) in mid-2008 was about 218.8. The CPI in
1930 (same base) was 16.7. The New York Yankees paid Babe Ruth $80,000 in 1930,
an enormous salary for an athlete in those days. The buying power of the Babe's salary
in 2008 dollars is about
A) $175,040. B) $202,100. C) $1,048,144. D) $1,336,000. E) $13,360,000.
23. The governments of all developed nations produce large volumes of data on economic
and social issues. Canada, like most countries, has a single national statistical office
(Statistics Canada) that is responsible for these data. In the United States,
A)
all federal statistics are handled by the Bureau
of Labor Statistics.
B)
there are separate statistical offices in each
federal agency (more than 70 of them).
C)
all data are produced by the states—there are
no federal statistical agencies.
D)
all data are produced by private firms—there
are no federal statistical agencies.
24. A pair of ballet slippers cost $35.00 in 1990; a pair of the same type of slippers costs
$105.00 in 2008. Using 1990 as the base year, what is the ballet slipper index number
for 2008?
A) 300 B) 0.33 C) 3.0 D) $35.00 E) $105.00
25. The price per pound of iceberg lettuce has
fluctuated quite a bit over the last few years.
Here it is in dollars, from 2002 to 2008:
$0.68
A) 2003
B) 2004
C) 2005
2002
2003
2004
2005
2006
$1.25
$0.82
$0.85
$0.90
In which of these years was the Iceberg
Lettuce Index Number (2002 = 100) equal to
120.6?
D) 2006 E) 2007
Use the following to answer questions 26-27:
There are separate CPIs for various components of the market basket. For example, the CPI for
new motor vehicles (1982–84 = 100) was 132.4 in 2008.
26. If there were no adjustments for quality improvements, then how much did new motor
vehicle rates increase from the base period to 1996?
A)
by 24%
B)
by 132.4%
C)
by a factor of about 1.3
D)
Both (B) and (C) are true.
E)
Impossible to say because the CPI doesn't
measure prices.
27. If there were adjustments in the new motor vehicle index due to quality improvements
(e.g., more features, better engines now than in 1984), would the increase in new motor
vehicle rates be greater, smaller, or the same as in the previous question?
A)
greater
D)
Could be either greater
or smaller.
B)
smaller
E)
The question doesn't
make sense.
C)
the same
The following question is related to question 75 in Chapter 12 and 71 in Chapter 13.
28. The Internal Revenue Service examines an SRS of 1,000 income tax returns. Because
of the shape of the distribution, you would describe this distribution numerically by
giving
A)
the mean and standard deviation.
B)
the correlation coefficient.
C)
incomes in real terms, using the CPI.
D)
the standard deviation and the correlation.
E)
the five-number summary.
29. The federal minimum wage was $6.55 an hour after it was increased in 2008. In 1980,
the minimum wage was $3.25 an hour. The CPI (1982–84 = 100) was 82.4 in 1980 and
was 218.8 in mid-2008. Which of these is true?
A)
The 1980 minimum wage is about $8.63 in
2008 dollars, so the minimum wage has gone
down in real terms.
B)
The 1980 minimum wage is about $8.63 in
2008 dollars, so the minimum wage has gone
up in real terms.
C)
The 1980 minimum wage is about $1.22 in
2008 dollars, so the minimum wage has gone
down in real terms.
D)
The 1980 minimum wage is about $1.22 in
2008 dollars, so the minimum wage has gone
up in real terms.
E)
The 1980 minimum wage is about $4.43 in
2008 dollars, so the minimum wage has gone
up in real terms.
30. The Consumer Price Index (1982–84 = 100) was about 207 in 2007. In 1989 the CPI
was 124. Tuition for in-state students at one Big Ten university was $2,032 in 1989. In
2007 dollars, this tuition is equivalent to
A)
2,032  {2007/1989} C)
2,032  {124/207} =
= $2,050.
$1,217.
B)
D)
2,032  {207/100} =
2,032  {207/124} =
$4,206.
$3,392.
31. The 2007 in-state tuition at the university in the previous question was $7,884. So your
calculation in the previous question shows that in the 1989–2007 period,
A)
tuition stayed the same C)
tuition went down in
B)
in real terms.
tuition went up in real D)
terms.
real terms.
Can't tell without more
information.
32. In the good old days (1986) the U.S. dollar was worth 1.85 Swiss Francs. Over two
decades later in 2008, the dollar was worth 1.16 Swiss Francs. The value of the dollar
in Swiss Francs went down by about
A)
69%.
B)
37%.
C)
59%.
D)
137%.
E)
Can't tell without knowing the CPI for 1986.
33. Suppose the CPI (Consumer Price Index) with respect to some unknown base period
was 89 in 1985, 115 in 1990, and 127 in 1993. The CPI rose steadily during this period.
The base period used
A)
must have been between 1985 and 1990.
B)
must have been between 1985 and 1993.
C)
must have been between 1990 and 1993.
D)
is 1982-1984 as usual.
E)
Can't tell from the information given.
Chapter 21
Use the following to answer questions 1-2:
A recent Gallup Poll asked, "Do you consider the amount of federal income tax you have to pay
as too high, about right, or too low?" 52% of the sample answered "Too high." Gallup says that:
“For results based on the sample of national adults (n = 1,021) surveyed April 6-9, 2008, the
margin of sampling error is  3 percentage points.”
1. The poll was carried out by telephone, so people without phones are always excluded
from the sample. Any errors in the final result due to excluding people without phones
A)
are included in the announced margin of error.
B)
are in addition to the announced margin of
error.
C)
can be ignored, because these people are not
part of the population.
D)
can be ignored, because this is a nonsampling
error.
2. If Gallup had used an SRS of size n =1021 and obtained the sample proportion p =
0.52 , you can calculate that the margin of error for 95% confidence would be
A)
D)
0.025 percentage
3,0 percentage
points.
points.
B)
E)
0.05 percentage
3.1 percentage
points.
points.
C)
1.6 percentage
points.
Use the following to answer questions 3-7:
The student newspaper at a college asks an SRS of 250 undergraduates, "Do you favor
eliminating supplemental fees for lab courses?" In all, 150 of the 250 are in favor.
3. The ___________ you want to estimate is the proportion p of all undergraduates who
favor eliminating the carnival.
A) bias B) confidence level C) mean D) parameter E) statistic
4. To estimate p, you will use the proportion p = 150/250 of your sample who favored
eliminating supplemental fees for lab courses. The number p is a
A) bias. B) confidence level. C) mean. D) parameter. E) statistic.
A)
B)
C)
5. A 95% confidence interval for the population proportion p is
D)
150  0.03.
E)
0.6  0.03.
150  0.06.
0.6  0.06.
1.67  0.03.
6. A 90% confidence interval based on this same sample would have
the same center and a larger margin of error.
the same center and a smaller margin of error.
a larger margin of error and probably a
different center.
D)
a smaller margin of error and probably a
different center.
E)
the same center, but the margin of error
changes randomly.
A)
B)
C)
7. Suppose that (unknown to you) 55% of all undergraduates favor eliminating
supplemental fees for lab courses. If you took a very large number of simple random
samples of size n = 250 from this population, the sampling distribution of the sample
proportion p would be normal with
A)
mean 0.55 and standard deviation 0.015.
B)
mean 0.60 and standard deviation 0.06.
C)
mean 0.55 and standard deviation 0.06.
D)
mean 0.60 and standard deviation 0.03.
E)
mean 0.55 and standard deviation 0.03.
8. You want to estimate the proportion of undergraduates at a college who favor
eliminating evening exams. You will choose an SRS. If you enlarge your SRS from
250 to 1000 students, the sample proportion p
A)
will have the same mean and the same standard
deviation.
B)
will have smaller bias and the standard
deviation will be 1/4 as large.
C)
will have smaller bias and the standard
deviation will be 1/2 as large.
D)
will have the same mean and the standard
deviation will be 1/4 as large.
E)
will have the same mean and the standard
deviation will be 1/2 as large.
9. The phrase "95% confidence" in a Gallup Poll press release means that
our results are true for 95% of the population
of all adults.
B)
95% of the population falls within the margin
of error we announce.
C)
the probability is 0.95 that a randomly chosen
adult falls in the margin of error we announce.
D)
we got these results using a method that gives
correct answers in 95% of all samples.
A)
Use the following to answer questions 10-12:
A recent Gallup Poll interviewed a random sample of 1,523 adults. Of these, 868 bought a lottery
ticket in the past year.
10. A 95% confidence interval for the proportion of all adults who bought a lottery ticket in
the past year is (assume Gallup used an SRS)
A)
D)
0.57  0.00016.
0.57  0.025.
B)
E)
0.57  0.00032.
0.57  0.03.
C)
0.57  0.013.
11. Suppose that in fact (unknown to Gallup) exactly 60% of all adults bought a lottery
ticket in the past year. If Gallup took many SRSs of 1,523 people, the sample
proportion who bought a ticket would vary from sample to sample. The sampling
distribution would be close to normal with
A)
mean 0.6 and standard deviation 0.00016.
B)
mean 0.6 and standard deviation 0.0126.
C)
mean 0.6 and standard deviation 0.4899.
D)
mean 0.6 and standard deviation 0.0251.
12. The same Gallup Poll asked its 1,523 adult respondents and also 501 teens (ages 13 to
17) whether they generally approved of legal gambling: 63% of adults and 52% of teens
said yes. The margin of error for a 95% confidence statement about teens would be
A)
greater than for adults, because the teen sample
is smaller.
B)
less than for adults, because the teen sample is
smaller.
C)
less than for adults, because there are fewer
teens in the population.
D)
the same as for adults, because they both come
from the same sample survey.
E)
Can't say, because it depends on what percent
of each population was in the sample.
Use the following to answer questions 13-15:
A surprising fact: 66% of all teenagers have a TV set in their room. If an opinion poll chooses an
SRS of 1,000 teens and asks if they have a TV set in their room, the percent who say "Yes" will
vary if the sample is repeated. In fact, the percent "Yes" in many samples will follow a normal
distribution with mean 66% and standard deviation 1.5%.
13. Which of these ranges of outcomes contains 95% of all the results of a large number of
polls of 1,000 teens?
A)
66% to 100%
C)
63% to 69%
B)
64.5% to 67.5%
D)
61.5% to 70.5%
14. Although the result will vary if the poll is repeated, the distribution of results is centered
at the truth about the population (66%). We call this desirable property of an SRS
A) lack of bias. B) low variability. C) symmetry. D) the confidence level.
15. The variation from sample to sample when the poll is repeated is described by the
standard deviation (1.5%). We would like this variation to be small, so that repeated
polls give almost the same result. To reduce the standard deviation, we could
A)
use an SRS of size less than 1,000.
B)
use an SRS of size greater than 1,000.
C)
use a confidence level less than 95%.
D)
use a confidence level greater than 95%.
E)
Both (B) and (C).
16. The margin of error for a 95% confidence interval is 2.8. If we decrease the confidence
level to 90%, the margin of error will be
A) biased. B) 99%. C) 2.8. D) smaller than 2.8. E) larger than 2.8.
17. For a 95% confidence interval, a larger sample size will generally give
a least-squares line.
D)
higher correlation.
a larger margin of
E)
a smaller margin of
error.
error.
C)
less bias.
A)
B)
18. If we take a simple random sample of size n = 500 from a population of size 500,000,
the variability of our estimate will be
A)
less than the bias.
B)
approximately the same as the variability for a
sample of size n = 500 from a population of
size 50,000,000.
C)
plus or minus 0.1%.
D)
much greater than the variability for a sample
of size n = 500 from a population of size
50,000,000.
E)
much less than the variability for a sample of
size n = 500 from a population of size
50,000,000.
19. We observe p = 0.4. If the standard deviation of the sampling distribution of p is 0.03,
what is the 95% confidence interval for p?
A)
0.37 to 0.43
D)
0.03 plus or minus 0.8
B)
0.31 to 0.39
E)
99% accurate
C)
0.4 plus or minus 0.06
The following two questions are related to question 44 in Chapter 4 and 73 in Chapter 14.
Use the following to answer questions 20-21:
Here are the attendance figures for the lectures in a large class.
20. 74% of the 398 students who attended the August 26 lecture said they knew how to "go
to a computer lab and get on the World Wide Web." If these 398 were a simple random
sample drawn from the entire student population, what would a 95% confidence interval
be for the percent of all students who could do likewise?
A)
D)
74%  0.05%
74%  4%
B)
E)
74%  2%
74%  0.04%
C)
74%  3%
21. In which of these cases would the confidence interval be wider than the one in the
previous question?
A)
if the confidence level were 90% instead of
95%
B)
C)
D)
if the sample size were 498 instead of 398
Both of the above.
Neither of the above.
22. A sample survey finds that 30% of a sample of 874 Ohio adults said good health was the
thing they were most thankful for. If that sample were an SRS from the population of all
Ohio adults, what would be the 99% confidence interval for the percent of all Ohio
adults who feel that way?
A)
25% to 35%
D)
28% to 32%
B)
26% to 34%
E)
29% to 31%
C)
27% to 33%
23. If the 874 people in the previous question had called a 900 number to give their
opinions, how would this affect your response?
A)
Not at all, because the width of the confidence
interval depends only on the sample size, and
not on the population size.
B)
Not at all, because the width of the confidence
interval depends only on the sample size, and
not on how the sample was obtained.
C)
It would be wider because voluntary response
polls have a bigger margin of error than SRSs.
D)
It would be narrower because voluntary
response polls are less variable than SRSs.
E)
A confidence interval makes no sense for a
voluntary response sample.
24. The name for the pattern of values that a statistic takes when we sample repeatedly from
the same population is
A)
the bias of the statistic.
B)
the sampling distribution of the statistic.
C)
the scale of measurement of the statistic.
D)
the variability of the statistic.
E)
the sampling error.
The following question is related to question 72 in Chapter 3 and 46 in Chapter 4.
25. A poll of 1,234 adults found that 62% expect an increase in environmental pollution in
the next decade. Take the poll's sample to be an SRS of all adults. Which of these is a
correct 95% confidence statement?
A)
B)
C)
D)
E)
With 95% confidence, the percent of the
sample who expect pollution to increase is
between 60.6% and 63.4%.
With 95% confidence, the percent of the
sample who expect pollution to increase is
between 59.2% and 64.8%.
With 95% confidence, the percent of all adults
who expect pollution to increase is between
60.6% and 63.4%.
With 95% confidence, the percent of all adults
who expect pollution to increase is between
59.2% and 64.8%.
With 95% confidence, the percent of all adults
who expect pollution to increase is between
59% and 65%.
26. A CBS News/New York Times opinion poll asked 1,190 adults whether they would prefer
balancing the federal budget over cutting taxes; 702 of those asked said "Yes." Take the
sample to be an SRS from the population of all adults. Which of these is a correct 95%
confidence interval for the proportion of all adults who prefer balancing the budget to
cutting taxes?
A)
D)
0.59  0.0004
0.59  0.0285
B)
E)
0.59  0.014
0.59  0.037
C)
0.59  0.0186
27. You choose an SRS of 2,000 women over 18 years of age from the New York City
metropolitan area; 623 of them are single. A 95% confidence interval for the proportion
of all adult women in the New York area who are single is (approximately)
A)
D)
0.31  0.03.
0.62  0.02.
B)
E)
0.62  0.03.
0.20  0.03.
C)
0.31  0.02.
28. An ad for ARCO graphite motor oil says (really): "Based on a 95% confidence level,
our tests achieved between 1% and 8.7% mileage improvement" as compared with a
conventional motor oil. What does the phrase "95% confidence level" mean here?
A)
ARCO graphite beats 95% of conventional
motor oils.
B)
The interval from 1% to 8.7% covers 95% of
the mileage improvements observed in the
tests.
C)
The tests included 95% of all oil brands on the
D)
E)
market.
The estimate that mileage improves
somewhere between 1% and 8.7% came from a
method that would catch the true improvement
in 95% of all similar tests.
A mistake has been made, because 95% +
8.7% is more than 100%.
Use the following to answer questions 29-32:
A poll of 1,190 adults found that 702 said they would prefer balancing the budget over cutting
taxes.
29. The sample proportion who prefer balancing the budget is
A)
unknown, because we only have information
on 1,190 people.
B)
unknown until we decide what confidence
level we want.
C)
1.70.
D)
0.59.
E)
0.41.
30. Suppose that the poll used an SRS. A 95% confidence interval for the proportion of all
adults who prefer balancing the budget to cutting taxes is
A)
D)
0.41  0.0285.
0.59  0.0004.
B)
E)
0.59  0.0285.
0.59  0.0143.
C)
0.41  0.0004.
31. A member of Congress thinks that 95% confidence isn't enough. He wants to be 99%
confident. How would the margin of error of a 99% confidence interval based on the
same sample compare with the 95% interval you found in the previous question?
A)
It would be smaller, because it omits only 1%
of the possible samples instead of 5%.
B)
It would be the same, because the sample is the
same.
C)
It would be larger, because higher confidence
requires a larger margin of error.
D)
Can't tell, because the margin of error is
random.
E)
Can't tell, because it depends on the size of the
population.
32. Another member of Congress is satisfied with 95% confidence, but she wants a smaller
margin of error. How can we get a smaller margin of error, still with 95% confidence?
A)
Take a larger sample, because larger samples
result in smaller margins of error.
B)
Take a smaller sample, because smaller
samples result in smaller margins of error.
C)
Take another sample of the same size and you
might be lucky and get a much smaller margin
of error.
D)
Take a sample of adults in Indiana instead of in
the entire country. Then the population will be
smaller and this will give a smaller margin of
error.
E)
Carry out a call-in poll to get a voluntary
response sample. Voluntary response samples
have no margin of error.
The following three questions are related to questions 78-79 in Chapter 3 and 50-52 in Chapter 4.
Use the following to answer questions 33-35:
The New York Times conducted a poll on women's issues in June of 1989.
33. One question asked was, "Many women have better jobs and more opportunities than
they did 20 years ago. Do you think women have had to give up too much in the
process, or not?" Of the 1,025 women who were asked, 492 said "Yes." Take these
1,025 women to be an SRS of all adult women. Which of these is a correct 95%
confidence interval for the proportion of all adult women who would say "Yes" to this
statement?
A)
D)
0.48  0.031
0.492  0.031
B)
E)
0.48  0.000487
0.492  0.0156
C)
0.48  0.0156
34. In the previous question, you obtained a 95% confidence interval for this telephone
sample. The bias due to leaving out people without a telephone
A)
is included in the margin of error.
B)
is not included in the margin of error, because
leaving out people with no phone is a
nonsampling error.
C)
is not included in the margin of error, because
D)
leaving out people with no phone has no effect
on the outcome of the poll.
is not included in the margin of error, because
the margin of error only covers the chance
variation in a random sample.
35. The 472 men were also asked the question, "Many women have better jobs and more
opportunities than they did 20 years ago. Do you think women have had to give up too
much in the process, or not?" above, and 212 of them said "Yes." The margin of error
for a 95% confidence interval for men would be
A)
larger than for women, because fewer men
were asked.
B)
smaller than for women, because fewer men
were asked.
C)
larger than for women, because fewer men said
"Yes."
D)
smaller than for women, because fewer men
said "Yes."
E)
the same as for women.
36. You are planning a survey of Pennsylvania households. Among other items, you will
ask whether they ate turkey on Thanksgiving day. You will give a 95% confidence
interval for the proportion p who ate turkey. If you take an SRS of 2,000 households,
the margin of error in your confidence interval will be
A)
twice as large as for an SRS of 500
households.
B)
one-half as large as for an SRS of 500
households.
C)
four times as large as for an SRS of 500
households.
D)
one-fourth as large as for an SRS of 500
households.
The following question is related to question 20 in Chapter 1, 80-81 in Chapter 3, and 55 in
Chapter 4.
37. A recent survey of 35,101 randomly selected U.S. adults studied the religious affiliation
of Americans. The survey interviewed 245 people in Maine. Suppose that this is a
simple random sample of adult residents of Maine. Of these 245 people, 56 said they
attend religious services at least once a week. A 95% confidence interval for the
proportion of all residents of Maine who attend religious services at least once a week is
closest to
A)
B)
0.202 to 0.256.
0.175 to 0.282.
C)
D)
0.215 to 0.242.
0.228 to 0.230.
38. If an SRS of size n = 1500 has sample proportion p = 0.55 approving of the president, a
95% confidence interval for the proportion p of all adults who approve is
A) 0.55  0.00033. B) 0.55  0.013. C) 0.55  0.026. D) 0.55  0.03.
The following question is related to questions 83-85 in Chapter 3 and 5-6 in Chapter 22.
39. In March 2000, the New York Times conducted "a telephone poll of a random sample of
1003 adults in all 50 states, giving all phone numbers, listed and unlisted, a
proportionate chance of being included." We can treat this as a simple random sample.
One question asked was, "Do you think what is shown on television today is less moral
than American society, more moral than American society, or accurately reflects
morality in American society?" Of the answers, 46% said "Less," 37% said "Accurate,"
9% said "More," and the others had no opinion. A 95% confidence interval for the
percent of all adults who think TV is less moral than society is about
A)
46%  2%.
B)
46%  3%.
C)
46%  4%.
D)
None of these, because we only have
information about a sample.
40. Most people can roll their tongues, but many
people can't. Whether or not a person can roll
his tongue is genetically determined. Suppose
we are interested in determining what fraction
of students can roll their tongues. We get a
simple random sample of 400 students and find
that 317 can roll their tongues. The margin of
error for a 95% confidence interval for the true
percentage of tongue-rollers among students is
closest to
A) 0.8%. B) 2.0%. C) 3.0%. D) 4.0%.
E) 20.75%.