Written review questions are on pages320-323 and 610-612 . Some on 610-612 are from chpt 9 not yet covered.
1. The standard deviation of 16 measurements of peoples weights (in pounds) is computed to be 5.4. The
variance of these measurements is
A) 2.24.
B) 29.16.
C) 52.34.
D) 256.
E) 21.6.
Use the following to answer question 2:
The timeplot below gives the number of burglaries committed each month for a city in Ohio. The plot is for the
three-year period January 1987–December 1989.
2. Which of the following is a true statement?
A) The number of burglaries in each month of 1988 were lower than the number of burglaries in each
month of 1989.
B) The median number of burglaries for a month in 1988 was a little over 25.
C) The total number of burglaries in 1989 was higher than in 1988.
D) None of the above.
E) More burglaries seem to be commited in June, July, and August during 1987, 1988, and 1989.
3. When drawing a histogram it is important to
A) have a separate class interval for each observation to get the most informative plot.
B) make sure the heights of the bars exceed the widths of the class intervals so that the bars are true
rectangles.
C) label the vertical axis so the reader can determine the counts or percent in each class interval.
D) leave large gaps between bars. This allows room for comments.
E) scale the vertical axis according to the variable whose distribution you are displaying.
Use the following to answer question 4:
For a physics course containing 10 students, the maximum point total for the quarter was 200. The point totals
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for the 10 students are given in the stemplot below.
4. The median point total for this class is
A) 130.
B) 130.5.
C) 133.
D) 134.4.
E) 137.
5. A reporter wishes to portray baseball players as overpaid. Which measure of center should he report as
the average salary of major league players?
A) The mean.
B) The median.
C) The mode.
D) Either the mean or median. It doesn't matter since they will be equal.
E) Neither the mean nor median. Both will be much lower than the actual average salary.
Use the following to answer question 6:
The following table presents data on wine consumption and death rate from heart attacks in 19 developed
Western countries.
WINE CONSUMPTION AND HEART ATTACKS
Country
Australia
Austria
Belgium
Canada
Denmark
Finland
France
Iceland
Ireland
Italy
Alcohol
from wine
2.5
3.9
2.9
2.4
2.9
0.8
9.1
0.8
0.7
7.9
Heart disease
Deaths
211
167
131
191
220
297
71
211
300
107
Country
Netherlands
New Zealand
Norway
Spain
Sweden
Switzerland
United Kingdom
United States
West Germany
Alcohol
from wine
1.8
1.9
0.8
6.5
1.6
5.8
1.3
1.2
2.7
Heart disease
Deaths
167
266
227
86
207
115
285
199
172
The distribution of heart disease death rates in these countries is close to this normal distribution:
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6. 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.
7. Using the standard normal distribution tables, the area under the standard normal curve corresponding to
0.5 < Z < 1.2 is
A) 0.3085.
B) 0.8849.
C) 0.5764.
D) 0.2815.
E) 0.3661.
8. Birthweights at a local hospital have a normal distribution with a mean of 110 oz. and a standard
deviation of 15 oz. The proportion of infants with birthweights under 95 oz. is
A) 0.500.
B) 0.159.
C) 0.341.
D) 0.841.
E) .025.
9. Using the standard normal distribution tables, the area under the standard normal curve corresponding to
Z > 1.22 is
A) 0.1151.
B) 0.1112.
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C) 0.4129.
D) 0.8849.
E) 0.8888.
10. 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 lower and upper 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.
Use the following to answer question 11:
The following table presents data on wine consumption and death rate from heart attacks in 19 developed
Western countries.
WINE CONSUMPTION AND HEART ATTACKS
Country
Australia
Austria
Belgium
Canada
Denmark
Finland
France
Iceland
Ireland
Italy
Alcohol
from wine
2.5
3.9
2.9
2.4
2.9
0.8
9.1
0.8
0.7
7.9
Heart disease
Deaths
211
167
131
191
220
297
71
211
300
107
Country
Netherlands
New Zealand
Norway
Spain
Sweden
Switzerland
United Kingdom
United States
West Germany
Alcohol
from wine
1.8
1.9
0.8
6.5
1.6
5.8
1.3
1.2
2.7
Here is a scatterplot of heart disease death rate versus wine consumption:
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Heart disease
Deaths
167
266
227
86
207
115
285
199
172
11. Which of the labeled points on the scatterplot represents Canada?
A) point a
B) point b
C) point c
D) point d
E) point e
Use the following to answer question 12:
Babies typically learn to crawl approximately six months after birth. However, it may take longer for babies to
learn to crawl in the winter when they are often bundled in clothes that restrict their movement. Thus there may
be an association between a baby's crawling age and the average temperature during the month they first try to
crawl. Below are the average ages (in weeks) at which babies began to crawl for a sample of babies born in
each of the twelve months of the year. In addition, the average temperature (in ºF) for the month that is six
months after the birth month is also listed.
Birth Month
January
February
March
April
May
June
July
August
September
October
November
December
Average Crawling Age Average Temperature
29.84
66
30.52
73
29.70
72
31.84
63
28.58
52
31.44
39
33.64
33
32.82
30
33.83
33
33.35
37
33.38
48
32.32
57
We want to investigate if the average age at which infants begin to crawl is influenced by the average outdoor
temperature six months after birth when they are likely to first begin crawling.
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12. Which of the following is a proper scatterplot of these data given the goals of the study?
A)
B)
C)
D)
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E) None of the above.
13. Scores on the 1995 SAT verbal aptitude test x among Kentucky high school seniors were normally
distributed with mean 420 and standard deviation 80. Scores on the 1995 SAT quantitative aptitude test
y among Kentucky high school seniors were normally distributed with mean 440 and standard deviation
60. The least-squares regression line has the equation
y = .6x + 188
The correlation between verbal scores and math scores is
A) .8
B) –.8
C) 0
D) can't be determined
14. A survey of midwest grain farms finds a correlation r = 0.42 between farm size (acres) and corn yield
(bushels) per acre. This means that
A) larger farms tend to have higher corn yields (per acre).
B) larger farms tend to have lower corn yields (per acre).
C) there is no connection between farm size and corn yield.
D) small farmers can invest more effort on each acre and therefore tend to have higher yields (per acre).
E) larger farmers should be given government subsidies to increase their productivity.
15. A student wonders if people of similar heights tend to date each other. She measures herself, her
dormitory roommate, and the women in the adjoining rooms; then she measures the next man each
woman dates. Here are the data (heights in inches):
Women 66
Men
72
64
68
66
70
65
68
70
74
65
69
Which of the following statements is true?
A) The variables measured are all categorical.
B) There is a strong negative correlation between the heights of men and women, since the women are
always smaller than the men they date.
C) There is a positive correlation between the heights of men and women.
D) Correlation makes no sense here since gender is a categorical variable.
E) Any height above 70 inches must be considered an outlier.
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16. Which of the following would be necessary to establish a cause-and-effect relation between two
variables?
A) Strong association between the variables.
B) An association between the variables is observed in many different settings.
C) The alleged cause is plausible.
D) There is no obvious lurking variable that would affect the response variable.
E) All of the above.
Use the following to answer questions 17-18:
A business has two types of employees, managers and workers. Managers earn either $100,000 or $200,000 per
year. Workers earn either $10,000 or $20,000 per year. The number of male and female managers at each
salary level and the number of male and female workers at each salary level are given in the two tables below.
$100,000
$200,000
Managers
Male
Female
80
20
20
30
$10,000
$20,000
Workers
Male
Female
30
20
20
80
17. The proportion of male managers who make $200,000 per year is
A) 0.067.
B) 0.133.
C) 0.200.
D) 0.400.
E) 0.667.
18. From these data we may conclude that
A) the mean salary of female managers is greater than that of male managers.
B) the mean salary of males in this business is greater than the mean salary of females.
C) the mean salary of female workers is greater than that of male workers.
D) this is an example of Simpson's Paradox.
E) All of the above.
19. A variable grows exponentially over time if
A) the variable increases by the addition of a fixed amount to the variable as time increases by a fixed
amount.
B) the variable increases by squaring its value whenever time is increased by a certain fixed amount.
C) the variable increases by multiplication by a fixed amount as time increases by a fixed amount.
D) the variable increases by the logarithm of its value whenever time is increased by a certain fixed
amount.
E) none of these.
20. According to the 1990 census, those states with an above-average number X of people who fail to
complete high school tend to have an above-average number Y of infant deaths. In other words, there is a
positive association between X and Y. The most plausible explanation for this association is
A) X causes Y. Thus programs to keep teens in school will help reduce the number of infant deaths.
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B) Y causes X. Thus programs that reduce infant deaths will ultimately reduce the number of high
school drop-outs.
C) lurking variables are probably present. For example, states with large populations will have both
larger numbers of people who fail to complete high school and a larger number of infant deaths.
D) both of these variables are directly affected by higher incidence of cancer in certain states.
E) the association between X and Y is purely coincidental. It is implausible to believe the observed
association could be anything other than accidental.
21. A candidate for mayor of Dallas calls 1,000 people chosen at random from the city telephone directory;
850 of them respond. What are the sampling frame and the sample in this example?
A) Sampling frame: the telephone directory. Sample: the 850 people who respond.
B) Sampling frame: the telephone directory. Sample: the 1,000 people who are called.
C) Sampling frame: the 1,000 people who are called. Sample: the 850 people who respond.
D) Sampling frame: all Dallas residents. Sample: the 1,000 people who are called.
E) Sampling frame: all Dallas residents. Sample: the 850 people who respond.
22. The essential difference between an experiment and an observational study is that
A) observational studies may have confounded variables, but experiments never do.
B) in an experiment, people must give their informed consent before being allowed to participate.
C) observational studies are always biased.
D) observational studies cannot have response variables.
E) an experiment imposes treatments on the subjects, but an observational study does not.
23. A simple random sample of 1200 adult Americans is selected, and each person is asked the following
question.
In light of the huge national deficit, should the government at this time spend additional money to
establish a national system of health insurance?
Only 39% of those responding answered yes. This survey
A) is reasonably accurate because it used a large, simple random sample.
B) probably overstates the percentage of people that favors a system of national health insurance.
C) probably understates the percentage of people that favors a system of national health insurance.
D) is very inaccurate, but neither understates nor overstates the percentage of people that favors a
system of national health insurance. Because simple random sampling was used, it is unbiased.
E) suffers from undercoverage bias.
Use the following to answer question 24:
You want to take an SRS of 50 of the 816 students who live in a dormitory on campus. You label the students
001 to 816 in alphabetical order. In the table of random digits you read the entries
95592 94007 69769 33547 72450 16632 81194 14873
24. The first three students in your sample have labels
A) 955, 929, 400.
B) 400, 769, 769.
C) 559, 294, 007.
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D) 929, 400, 769.
E) 400, 769, 335.
25. The general term for the kind of samples recommended by statisticians is probability sample. Which of
these are accurate statements about probability samples of n individuals?
A) All samples of size n can be chosen, and all have the same chance to be chosen.
B) There may be some samples of size n that can't be chosen.
C) There may be samples of size n that can be chosen, but have different chances to be chosen.
D) Both (B) and (C) are true.
E) None of these statements is true.
26. I select two cards from a deck of 52 cards and observe the color of each (26 cards in the deck are red and
26 are black). Which of the following is an appropriate sample space S for the possible outcomes?
A) S = {red, black}
B) S = {(red, red), (red, black), (black, red), (black, black)}, where, for example, (red, red) stands for
the event "the first card is red and the second card is red."
C) S = {(red, red), (red, black), (black, black)}, where, for example, (red, red) stands for the event "the
first card is red and the second card is red."
D) S = {0, 1, 2}.
E) All of the above.
Use the following to answer question 27:
An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both
A and B will occur is 0.1.
27. The conditional probability of A given B
A) is 0.5.
B) is 0.3.
C) is 0.2.
D) is 1/6.
E) cannot be determined from the information given.
28. You read in a book about bridge that the probability that each of the four players is dealt exactly one ace
is about 0.11. This means that
A) in every 100 bridge deals, each player has one ace exactly 11 times.
B) in one million bridge deals, the number of deals on which each player has one ace will scarcely be
within ±100 of 110,000.
C) in a very large number of bridge deals, the percent of deals on which each player has one ace will be
very close to 11%.
D) in a very large number of bridge deals, the average number of aces in a hand will be very close to
0.11.
29. The collection of all possible outcomes of a random phenomenon is called
A) a census.
B) the probability.
C) a chance experiment
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D) the sample space.
E) the distribution.
30. If the knowledge that an event A has occurred implies that a second event B cannot occur, the events A
and B are said to be
A) independent.
B) disjoint.
C) mutually exhaustive.
D) the sample space.
E) complementary.
Use the following to answer question 31:
The weight of medium-sized tomatoes selected at random from a bin at the local supermarket is a random
variable with mean µ = 10 ounces and standard deviation  = 1 ounce.
31. Suppose we pick four tomatoes from the bin at random and put them in a bag. The weight of the bag is
a random variable with a standard deviation (in ounces) of
A) 0.25.
B) 0.50.
C) 1.0.
D) 4.0.
E) none of these, because the numbers are not independent.
32. The probability distribution for the number of heads in four tosses of a coin is given by
Let X represent the number of heads. The probability of at least one tail is given by
A) P(X  3).
B) P(X  3).
C) P(X < 3).
D) P(X > 3).
E) P(X  1).
Use the following to answer question 33:
A small store keeps track of the number X of customers that make a purchase during the first hour that the store
is open each day. Based on the records, X has the following probability distribution.
33. Suppose the store is open seven days per week from 8:00 a.m. to 5:30 p.m. The mean number of
customers that make a purchase during the first hour that the store is open during a one-week period is
A) 3.0.
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B)
C)
D)
E)
9.0.
19.0.
21.0.
28.0.
34. The weight of reports produced in a certain department has a normal distribution with mean 60 g and
standard deviation 12 g. The probability that the next report will weigh less than 45 g is
A) .1056.
B) .3944.
C) .1042.
D) .0418.
E) .8944.
Use the following to answer question 35:
The probability density of a random variable X is given in the figure below.
35. The probability that X is at least 1.5 is
A) 0.
B) 1/4.
C) 1/3.
D) 1/2.
E) 3/4.
Use the following to answer question 36:
There are twenty multiple-choice questions on an exam, each having responses a, b, c, or d. Each question is
worth five points and only one option per question is correct. Suppose the student guesses the answer to each
question, and the guesses from question to question are independent.
36. The distribution of X, the number of questions the student will get correct, is
A) binomial with parameters n = 5 and p = 0.2.
B) binomial with parameters n = 20 and p = 0.25.
C) binomial with parameters n = 5 and p = 0.25.
D) binomial with parameters n = 4 and p = 0.25.
E) none of these.
37. In a certain game of chance, your chances of winning are 0.2. If you play the game five times and
outcomes are independent, the probability that you win all five times is
A) 0.6723.
B) 0.3277.
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C) 0.32.
D) 0.04.
E) 0.00032.
38. As part of a promotion for a new type of cracker, free trial samples are offered to shoppers in a local
supermarket. The probability that a shopper will buy a packet of crackers after tasting the free sample is
0.20. Different shoppers can be regarded as independent trials. If X is the number of the next 100
shoppers that buy a packet of the crackers after tasting a free sample, then the probability that X exceeds
25 is approximately
A) 0.0438.
B) 0.1056.
C) 0.3773.
D) 0.9125.
E) 0.9562.
Use the following to answer questions 39-40:
A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5%
to 6%, with the additional revenue going to education. Let X denote the number in the sample that say they
support the increase. Suppose that 40% of all adults in Ohio support the increase.
39. The probability that X is more than 650 is
A) less than 0.0001.
B) less than 0.001.
C) less than 0.01.
D) 0.9960.
E) none of these.
40. The mean  of X is
A) 5%.
B) 360.
C) 0.40.
D) 600.
E) 90.
41. The sampling distribution of a statistic is
A) the probability that we obtain the statistic in repeated random samples.
B) the mechanism that determines whether or not randomization was effective.
C) the distribution of values taken by a statistic in all possible samples of the same size from the same
population.
D) the extent to which the sample results differ systematically from the truth.
E) approximately normal.
42. The distribution of values taken by a statistic in all possible samples of the same size from the same
population is the
A) probability that the statistic is obtained.
B) population parameter.
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C) variance of the values.
D) sampling distribution of the statistic.
E) same shape as the population distribution.
43. The variability of a statistic is described by
A) the spread of its sampling distribution.
B) the amount of bias present.
C) the vagueness in the wording of the question used to collect the sample data.
D) probability calculations.
E) the stability of the population it describes.
44. The incomes in a certain large population of college teachers have a normal distribution with mean
$35,000 and standard deviation $5000. Four teachers are selected at random from this population to
serve on a salary review committee. What is the probability that their average salary exceeds $40,000?
A) 0.0228
B) 0.1587
C) 0.8413
D) 0.9772
E) essentially 0
Use the following to answer question 45:
A simple random sample of 50 undergraduates at Johns Hopkins University found that 60% of those sampled
felt that drinking was a problem among college students. A simple random sample of 50 undergraduates at
Ohio State University found that 70% felt that drinking was a problem among college students. The number of
undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State is
approximately 40,000. Suppose the actual proportion of undergraduates at Johns Hopkins University who feel
drinking is a problem among college students is 70%.
45. Are the conditions for using normal approximation satisfied for both of these surveys?
A) Yes.
B) No. The conditions are satisified for Johns Hopkins, but not for Ohio State.
C) No. The conditions are satisified for Ohio State, but not for Johns Hopkins.
D) No. The sample size of 50 is not large enough.
E) No. There is bias in the question.
46. A simple random sample of 1000 Americans found that 61% were satisfied with the service provided by
the dealer from which they bought their car. A simple random sample of 1000 Canadians found that
58% were satisfied with the service provided by the dealer from which they bought their car. The
sampling variability associated with these statistics is
A) exactly the same.
B) smaller for the sample of Canadians because the population of Canada is smaller than that of the
United States, hence the sample is a larger proportion of the population.
C) smaller for the sample of Canadians because the percentage satisfied was smaller than that for the
Americans.
D) larger for the Canadians because Canadian citizens are more widely dispersed throughout the
country than in the United States, hence they have more variable views.
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E) about the same.
47. Suppose you are going to roll a die 60 times and record p, the proportion of times that a 1 or a 2 is
showing. The sampling distribution of p should be centered about
A) 1/6.
B) 1/3.
C) 1/2.
D) 20.
E) 30.
Use the following to answer questions 48-49:
Below are histograms of the the values taken by three sample statistics in several hundred samples from the
same population. The true value of the population parameter is marked on each histogram.
48. Based on the performance of the three statistics in many samples, which is preferred as an estimate of
the parameter?
A) statistic A.
B) statistic B.
C) statistic C.
D) either A or B would be equally good.
E) either B or C would be equally good.
49. The statistic that has the largest bias among these three is
A) statistic A.
B) statistic B.
C) statistic C.
D) A and B have similar bias, and it is larger than the bias of C.
E) B and C have similar bias, and it is larger than the bias of A.
Use the following to answer question 50:
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The distribution of actual weights of 8-oz. chocolate bars produced by a certain machine is normal with mean
8.1 ounces and standard deviation 0.1 ounces.
50. If a sample of five of these chocolate bars is selected, there is only a 5% chance that the average weight
of the sample of five of the chocolate bars will be below
A) 7.84 oz.
B) 7.94 oz.
C) 8.03 oz.
D) 8.08 oz.
E) 8.17 oz.
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Answer Key -- 2003-2004 Final Review
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
B
C
C
B
A
C
C
B
E
D
A
A
A
A
C
E
C
E
C
C
A
E
C
E
D
B
D
C
D
B
B
B
D
A
B
B
E
B
C
D
C
D
A
A
A
46. E
47.
B
48.
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A
49.
D
50.
C