Name: ______________________
Class: _________________
Date: _________
ID: A
AP Statistics Midterm
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Scenario 1-1
A review of voter registration records in a small town yielded the following table of the number of males and
females registered as Democrat, Republican, or some other affiliation.
Democrat
Republican
Other
Male
300
500
200
Female
600
300
100
1. Use Scenario 1-1. Which of the following graphs accurately represents the distribution for political party
registration for each gender?
A.
D.
B.
E.
C.
1
Name: ______________________
ID: A
2. A particularly common question in the study of wildlife behavior involves observing contests between
"residents" of a particular area and "intruders." In each contest, the "residents" either win or lose the
encounter (assuming there are no ties). Observers might record several variables, listed below. Which of these
variables is categorical?
A. The duration of the contest (in seconds).
B. The number of animals involved in the contest.
C. Whether the "residents" win or lose.
D. The total number of contests won by the "residents."
E. None of these.
Scenario 1-2
Below is a two-way table summarizing the number of cylinders in selected car models manufactured in six
different countries in the 1990’s.
France
Germany
Italy
Japan
Sweden
U.S.A.
Total
Number of cylinders
4
5
6
8
0
0
1
0
4
1
0
0
1
0
0
0
6
0
1
0
1
0
1
0
7
0
7
8
19
1
10
8
Total
1
5
1
7
2
22
38
3. Use Scenario 1-2. The percentage of all cars listed in the table with 4-cylinder engines is
A. 19%.
B. 21%.
C. 50%.
D. 80%.
E. 91%.
4. A set of data has a mean that is much larger than the median. Which of the following statements is most
consistent with this information?
A. The distribution is symmetric.
D. The distribution is bimodal.
B. The distribution is skewed left.
E. The data set has a few low outliers.
C. The distribution is skewed right.
5. The standard deviation of 16 peoples’ weights (in pounds) is computed to be 5.4. The units for the variance
of these measurements is
A. pounds.
D. no units. Variance never has units.
B. square root pounds.
E. percentiles.
C. pounds squared.
6. You catch 10 cockroaches in your bedroom and measure their lengths in centimeters. Which of these sets of
numerical descriptions are all measured in centimeters?
A. median length, variance of lengths, largest length
B. median length, first and third quartiles of lengths
C. mean length, standard deviation of lengths, median length
D. mean length, median length, variance of lengths.
E. both (B) and (C)
2
Name: ______________________
ID: A
7. You can roughly locate the median 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.
E. the point at which the height of the graph is equal to 1.
8. Here is a list of exam scores for Mr. Williams’s calculus class:
60
61
61
65
72
75
75
78
81
81
What is the percentile of the person whose score was 85?
A. 15%
B. 21%
C. 29%
D. 71%
85
89
91
98
E. 85%
9. The Normal curve below describes the death rates per 100,000 people in developed countries in the 1990’s.
The
A.
B.
C.
D.
E.
mean and standard deviation of this distribution are approximately
Mean 100; Standard Deviation 65
Mean 100; Standard Deviation 100
Mean 190; Standard Deviation 65
Mean 190; Standard Deviation 100
Mean 200; Standard Deviation 130
10. 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 about
A. 0.159.
B. 0.025.
C. 0.341.
D. 0.500.
E. 0.841.
11. Two variables are said to be negatively associated if
A. larger values of one variable are associated with larger values of the other.
B. larger values of one variable are associated with smaller values of the other.
C. smaller values of one variable are associated with smaller values of the other.
D. smaller values of one variable are associated with both larger or smaller values of the
other.
E. there is no pattern in the relationship between the two variables.
12. 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?
A. 1"
B. 3"
C. 4"
D. 6"
E. 12"
13. The card game Euchre uses a deck with 32 cards: Ace, King, Queen, Jack, 10, 9, 8, 7 of each suit. Suppose
you choose one card at random from a well-shuffled Euchre deck. What is the probability that the card is a
Jack, given that you know it’s a face card?
A. 1/3
B. 1/4
C. 1/8
D. 1/9
E. 1/12
3
Name: ______________________
ID: A
14. 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.
15. When a basketball player makes a pass to a teammate who then scores, he earns an “assist.” Below is a
Normal probability plot for the number of assists earned by all players in the National Basketball Association
during the 2010 regular season.
Which of the following statements about the shape of this distribution is true?
A. The distribution is Normal.
B. The distribution is approximately Normal.
C. The distribution is roughly symmetric.
D. The distribution has no potential outliers.
E. The distribution is skewed.
16. The fraction of the variation in the values of a response y that is explained by the least-squares regression of
y on x is the
A. correlation coefficient.
B. slope of the least-squares regression line.
C. square of the correlation coefficient.
D. intercept of the least-squares regression line.
E. sum of the squared residuals.
4
Name: ______________________
ID: A
Scenario 3-2
The following table and scatter plot present data on wine consumption (in liters per person per year) and
death rate from heart attacks (in deaths per 100,000 people per year) in 19 developed Western countries.
Country
Australia
Austria
Belgium
Canada
Denmark
Finland
France
Iceland
Ireland
Italy
Wine Consumption
Alcohol from Heart
wine
disease
deaths
2.5
211
3.9
167
2.9
131
2.4
191
2.9
220
0.8
297
9.1
71
0.8
0.7
7.9
211
300
107
and Heart Attacks
Country
Alcohol from
wine
Netherlands
New Zealand
Norway
Spain
Sweden
Switzerland
United
Kingdom
United States
West Germany
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
115
285
199
172
17. Use Scenario 3-2. If heart disease death rate were expressed as deaths per 1,000 people instead of as deaths
per 100,000 people, how would the correlation r between wine consumption and heart disease death rate
change?
A. r would be divided by 100.
D. r would be multiplied by 10.
B. r would be divided by 10.
E. r would be multiplied by 100.
C. r would not change.
18. The
A.
B.
C.
collection of all possible outcomes of a random phenomenon is called
a census.
D. the sample space.
the probability.
E. the distribution.
a chance experiment
5
Name: ______________________
19. The
A.
B.
C.
D.
E.
ID: A
most important advantage of experiments over observational studies is that
experiments are usually easier to carry out.
experiments can give better evidence of causation.
confounding cannot happen in experiments.
an observational study cannot have a response variable.
observational studies cannot use random samples.
20. Consider the following scatter plot of two variables, X and Y.
We
A.
B.
C.
D.
E.
may conclude that the correlation between X and Y
must be close to –1, since the relationship is between X and Y is clearly non-linear.
must be close to 0, since the relationship is between X and Y is clearly non-linear.
is close to 1, even though the relationship is not linear.
may be exactly 1, since all the points line of the same curve.
greater than 1, since the relationship is non-linear.
21. A study of elementary school children, ages 6 to 11, finds a high positive correlation between shoe size x and
score y on a test of reading comprehension. The observed correlation is most likely due to
A. the effect of a lurking variable, such as age.
B. a mistake, since the correlation must be negative.
C. cause and effect (larger shoe size causes higher reading comprehension).
D. "reverse" cause and effect (higher reading comprehension causes larger shoe size.
E. several outliers in the data set.
6
Name: ______________________
ID: A
Scenario 3-4
Consider the following scatterplot of amounts of CO (carbon monoxide) and NOX (nitrogen oxide) in grams
per mile driven in the exhausts of cars. The least-squares regression line has been drawn in the plot.
22. Use Scenario 3-4. The intercept of the least-squares regression line is approximately
A. –0.7.
B. –0.1.
C. 1.8.
D. 2.0.
E. 18.
23. The correlation between the age and height of children is found to be about r = 0.7. Suppose we use the age x
of a child to predict the height y of the child. We conclude that
A. the least-squares regression line of y on x would have a slope of 0.7.
B. the fraction of the variation in heights explained by the least-squares regression line
of y on x is 0.49.
C. about 70% of the time, age will accurately predict height.
D. the fraction of the variation in heights explained by the least-squares regression line
of y on x is 0.70.
E. the line explains about 49% of the data.
24. Which of the following statements concerning residuals is true?
A. The sum of the residuals is always 0.
B. A plot of the residuals is useful for assessing the fit of the least-squares regression line.
C. The value of a residual is the observed value of the response minus the value of the
response that one would predict from the least-squares regression line.
D. An influential point on a scatterplot is not necessarily the point with the largest
residual.
E. All of the above.
25. In order to assess the opinion of students at the University of Minnesota on campus snow removal, a reporter
for the student newspaper interviews the first 12 students he meets who are willing to express their opinion.
The method of sampling used is
A. a census
D. a convenience sample
B. a systematic sample
E. a simple random sample
C. a voluntary sample
7
Name: ______________________
ID: A
Scenario 3-8
A fisheries biologist studying whitefish in a Canadian Lake collected data on the length (in centimeters) and
egg production for 25 female fish. A scatter plot of her results and computer regression analysis of egg
production versus fish length are given below.
Note that Number of eggs is given in thousands (i.e., “40” means 40,000 eggs).
Predictor
Constant
Fish length
S = 6.75133
26. Use
A.
B.
C.
Coef
-142.74
39.250
SE Coef
25.55
5.392
R-Sq = 69.7%
T
-5.59
7.28
P
0.000
0.000
R-Sq(adj) = 68.4%
Scenario 3-8. The equation of the least-squares regression line is
Eggs = –142.74 + 39.25(Length)
D. Eggs = 25.55 + 5.392(Eggs)
Eggs = 39.25 – 142.74(Length)
E. Eggs = –142.74 + 39.25(Eggs)
Eggs = 25.55 + 5.392(Length)
27. In probability and statistics, a random phenomenon is
A. something that is completely unexpected or surprising
B. something that has a limited set of outcomes, but when each outcome occurs is
completely unpredictable.
C. something that appears unpredictable, but each individual outcome can be accurately
predicted with appropriate mathematical or computer modeling.
D. something that is unpredictable from one occurrence to the next, but over the course
of many occurrences follows a predictable pattern
E. something whose outcome defies description.
Scenario 5-5
Suppose we roll two six-sided dice--one red and one green. Let A be the event that the number of spots
showing on the red die is three or less and B be the event that the number of spots showing on the green die is
three or more.
28. Use Scenario 5-5. P(A ∪ B) =
A. 1/6.
B. 1/4.
C. 2/3.
D. 5/6.
8
E. 1.
Name: ______________________
ID: A
29. You plan to give a math achievement test to samples of 15 year-olds from both the U.S. and Korea in order
to compare mathematics knowledge in the two countries. In each country, you will randomly choose
300 students from low-income families
400 students from middle-income families
200 students from high-income families
The
A.
B.
C.
sample from Korea is a
multistage sample.
simple random sample.
convenience sample.
D. voluntary response sample.
E. stratified random sample.
Scenario 4-5
In order to assess the effects of exercise on reducing cholesterol, a researcher took a random sample of fifty
people from a local gym who exercised regularly and another random sample of fifty people from the
surrounding community who did not exercise regularly. They all reported to a clinic to have their cholesterol
measured. The subjects were unaware of the purpose of the study, and the technician measuring the
cholesterol was not aware of whether or not subjects exercised regularly.
30. Use
A.
B.
C.
D.
E.
Scenario 4-5. This is a(n)
observational study.
experiment, but not a double blind experiment.
double blind experiment.
matched pairs experiment.
block design.
Scenario 5-11
The following table compares the hand dominance of 200 Canadian high-school students and what methods
they prefer using to communicate with their friends.
Left-handed
Right-handed
Total
Cell phone/Text
12
43
55
In person
13
72
85
Online
9
51
60
Total
34
166
200
Suppose one student is chosen randomly from this group of 200.
31. Use Scenario 5-11. What is the probability that the student chosen is left-handed or prefers to communicate
with friends in person?
A. 0.065
B. 0.17
C. 0.425
D. 0.53
E. 0.595
32. In comparative trials in medicine, the placebo effect and subconscious bias on the part of the physicians
evaluating treatment outcomes can be avoided by using
A. the double-blind technique.
D. stratified random samples.
B. randomized complete block designs.
E. all of the above.
C. response variables.
9
Name: ______________________
ID: A
Scenario 4-7
A farmer wishes to determine which of two brands of baby pig pellets, Kent or Moormans, produces better
weight gains. Two of his sows each give birth to litters of 10 pigs on the same day, so he decides to give the
baby pigs in litter A only Kent pellets, while the pigs in litter B will get only Moormans pellets. After four
weeks, the average weight gain for pigs in litter A is greater than the average weight gain for pigs in litter B.
33. Use
A.
B.
C.
D.
E.
Scenario 4-7. The farmer has conducted a(n)
stratified random sample.
matched pairs design.
observational study.
experiment, but not a completely randomized experiment.
completely randomized experiment.
34. Use Scenario 4-7. If the farmer had fed Kent pellets to an SRS of 5 pigs from litter A and an SRS of 5 pigs
from litter B, with the remaining 10 pigs getting Moormans pellets, then he would have been using
A. a systematic random sample.
D. a block design.
B. a convenience sample.
E. a completely randomized design.
C. a matched-pairs design.
35. When two coins are tossed, the probability of getting two heads is 0.25. This means that
A. of every 100 tosses, exactly 25 will have two heads.
B. the odds against two heads are 4 to 1.
C. in the long run, the average number of heads is 0.25.
D. in the long run two heads will occur on 25% of all tosses.
E. if you get two heads on each of the first five tosses of the coins, you are unlikely to
get heads the fourth time.
36. A poker player is dealt poor hands for several hours. He decides to bet heavily on the last hand of the evening
on the grounds that after many bad hands he is due for a winner.
A. He's right, because the winnings have to average out.
B. He's wrong, because successive deals are independent of each other.
C. He's right, because successive deals are independent of each other.
D. He's wrong, because he’s clearly on a “cold streak.”
E. Whether he’s right or wrong depends on how many bad hands he’s been dealt so far.
37. A stack of four cards contains two red cards and two black cards. I select two cards, one at a time, and do not
replace the first card selected before selecting the second card. Consider the events
A = the first card selected is red
The
A.
B.
C.
D.
E.
B = the second card selected is red
events A and B are
independent and disjoint.
not independent, but disjoint.
independent, not disjoint
not independent, not disjoint.
independent, but we can’t tell it’s disjoint without further information.
10
Name: ______________________
ID: A
38. A basketball player makes 75% of his free throws. We want to estimate the probability that he makes 4 or
more frees throws out of 5 attempts (we assume the shots are independent). To do this, we use the digits 1, 2,
and 3 to correspond to making the free throw and the digit 4 to correspond to missing the free throw. If the
table of random digits begins with the digits below, how many free throw does he hit in our first simulation of
five shots?
19223 95034 58301
A. 1
B. 2
C. 3
D. 4
E. 5
Scenario 5-8
A student is chosen at random from the River City High School student body, and the following events are
recorded:
M = The student is male
F = The student is female
B = The student ate breakfast that morning.
N = The student did not eat breakfast that morning.
The following tree diagram gives probabilities associated with these events.
39. Use Scenario 5-8. Given that a student who ate breakfast is selected, what is the probability that he is male?
A. 0.32
B. 0.40
C. 0.50
D. 0.64
E. 0.80
Scenario 5-12
The letters p, q, r, and s represent probabilities for the four distinct regions in the Venn diagram below. For
each question, indicate which expression describes the probability of the event indicated.
40. Use Scenario 5-12.
A. p
B. r
C. q + s
D. q + s – r
11
E. q + s + r
Name: ______________________
ID: A
41. The following histogram represents the distribution of acceptance rates (percent accepted) among 25 business
schools in 1997.
What percent of the schools have an acceptance rate of under 20%?
A. 3%
B. 4%
C. 12%
D. 16%
42. The
The
A.
B.
E. 24%
mean age of four people in a room is 30 years. A new person whose age is 55 years enters the room.
mean age of the five people now in the room is
30.
C. 37.5.
E. Cannot be determined
35.
D. 40.
43. A data set is Normally distributed with a mean of 25 and a standard deviation of 8. If you calculate the
standard score of every observation in this data set, the resulting scores will have a distribution that has
A. mean of 100; standard deviation of 10. D. mean of 1; standard deviation of 1.
B. mean of 25; standard deviation of 10.
E. mean of 0; standard deviation of 1.
C. mean of 25; standard deviation of 1.
Scenario 3-5
In a statistics course a linear regression equation was computed to predict the final exam score from the score
on the first test. The equation of the least-squares regression line was
where
represents the
predicted final exam score and x is the score on the first exam.
44. Use Scenario 3-5. Suppose Joe scores a 90 on the first exam. What would be the predicted value of his score
on the final exam?
A. 91
C. 89
E. Cannot be determined
B. 90
D. 81
45. A local tax reform group polls the residents of the school district and asks the question, “Do you think the
school board should stop spending taxpayers’ money on non-essential arts programs in elementary schools?”
The results of this poll are likely to
A. Underestimate support for arts programs because of undercoverage.
B. Underestimate support for arts programs because of nonsampling error.
C. Overestimate support for arts programs because of undercoverage.
D. Overestimate support for arts programs because of nonsampling error.
E. Accurately estimate support for arts programs.
12