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AP Multiple Choice Review 1-100
1. A magazine has 1,620,000 subscribers, of whom 640,000 are women and 980,000 are men. Thirty percent of the women read the
advertisements in the magazine and 50 percent of the men read the advertisements in the magazine. If a random sample of 100 subscribers
is selected, what is the expected number of subscribers in the sample who read the advertisements?
(A) 30
(B) 40
(C) 42
(D) 50
(E) 80
2. A manufacturer makes light bulbs and claims that their reliability is 98 percent. Reliability is defined to be the proportion of nondefective items that are produced over the long term. If the company’s claim is correct, what is the expected number of non-defective light
bulbs in a random sample of 1,000 bulbs?
(A) 20
(B) 200
(C) 960
(D) 980
(E) 1,000
3. When a virus is placed on a tobacco leaf, small lesions appear on the leaf. To compare the mean number of lesions produced by two
different strains of virus, one strain is applied to half of each of 8 tobacco leaves, and the other strain is applied to the other half of each
leaf. The strain that goes on the right half of the leaf is decided by a flip of a coin. The lesions that appear on each half are then counted.
The data are given below:
LEAF
1
2
3
4
5
6
7
8
STRAIN1
31 20 18 17 9
8
10 7
STRAIN 2
18 17 14 11 10
7
5
6
What is the number of degrees of freedom associated with the appropriate t-test for testing to see if there is a difference between the mean
number of lesions per leaf produced by the two strains?
(A) 7
(B) 8
(C) 11
(D) 14
(E) 16
4. In a cluster sample:
(A) We randomly select subsets of the population and sample everyone in that subset
(B) An alphabetic list of individuals is used for random selection into the sample.
(C) Individuals are distinguished based on some characteristic such as gender before they are randomly selected from the population
(D) Only convenient members of the population are chosen
(E) None of the above
5. Which of the following can be used to show a cause-and-effect relationship between two variables?
(A) A census
(B) A controlled experiment
(C) An observational study
(D) A sample survey
(E) A cross-sectional survey
6. The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If
Rachel is at the 90th percentile in height for adult women, then her height, in inches, is closest to:
(A) 60
(B) 62
(C) 68
(D) 70
(E) 74
7. Sara and Ryan plan to visit a bookstore. Based on their previous visits to this bookstore, the probability distributions of the numbers of
books they will buy are given below:
X = Number of books Sara will buy
Y = Number of books Ryan will buy
X
0
1
2
Y
0
1
2
P(X) 0.50 0.25
0.25
P(Y) 0.25 0.50 0.25
Assuming that Sara and Ryan make their decisions independently, what is the probability that they will purchase no books on this visit to
the bookstore?
(A) 0.0625 (B) 0.1250
(C) 0.1875
(D) 0.2500
(E) 0.7500
8. Joan’s doctor told her that the standardized score (Z-score) for her systolic blood pressure, as compared to the blood pressure of other
women her age, is 1.50. Which of the following is the best interpretation of this standardized score?
(A) Joan’s systolic blood pressure is 150
(B) Joan’s systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women her age.
(C) Joan’s systolic blood pressure is 1.50 above the average systolic blood pressure of women her age.
(D) Joan’s systolic blood pressure is 1.50 times the average systolic blood pressure of women her age.
(E) Only 1.5% of women Joan’s age have a higher systolic blood pressure than she does.
9. Every Thursday, Thomas and Sean Video Venture has “roll the dice” day. A customer may choose to roll two fair dice and rent a
second movie for an amount (in cents) equal to the numbers uppermost on the dice with the larger number first. For example, if the
customer rolls a 2 and a 4, a second movie may be rented for $0.42. If a 2 and a 2 are rolled, a second movie may be rented for $0.22. Let
X represent the amount paid for a second movie on roll the dice day. The expected value
of X is $0.47 and the standard deviation of X is $0.15.
If a customer rolls a dice and rents a second movie every Thursday for 20 consecutive weeks, what is the total amount that the customer
would expect to pay for these second movies?
(A) $0.45
(B) $0.47
(C) $0.67
(D) $3.00
(E) $9.40
10. A sampling distribution of the means of all possible samples of size 100 is formed. The parent population has a mean of μ = 4.2 and a
standard deviation of σ= 1.7. What is the value of the standard error of the mean?
(A) 0.017
(B) 0.17
(C)0.42
(D) 1.7
(E) 4.2
11. Anthropologists must often estimate from human remains how tall a person was when alive. To do this they study how overall height
can be predicted from the length of a leg bone in a group of 36 living males. The data show that the bone lengths have a mean of 45.9
centimeters and the standard deviation of 4.20 cm. Overall the height for the same men has standard deviation of 8.14 cm. The
correlation between bone length and height is 0.914. The slope of the least squares regression line of height on bone length is about:
(A) 0.47
(B) 1.77
(C) 151.1
(D) 91.5
12. Near election time, the Gallop Poll increases the size of its samples from about 1500 people to about 4000 people. The purpose of this
is:
(A) To reduce the bias of the result
(B) To increase the bias of the result
(C) To reduce the variability of the result
(D) To increase the variability of the result.
13. Mr. Roger’s wants to curve student’s exam scores based on the highest score in the class. He takes the highest score (which happens
to be an outlier) and treats it as the perfect score. He then computes everyone else’s score as a percentage of this perfect score. You’re
smart and complain that his method is not resistant. What would be a more resistant method of grading these exams?
(A) Grading scores relative to the mean score.
(B) Treating the top two scores as the perfect score.
(C) Computing an individual’s score relative to the mode.
(D) Grading scores relative to the median score.
(E) All of the above
14. An industrial experiment compares the degree of micro-porosity (which eventually leads to cracks and failure in use) in aluminum
alloy produced under two conditions. Ultrasound measurements of 5 ingots produced by the first method give mean of 4.4 and standard
deviation of 0.8. Similar measurements on 6 ingots produced by the second method have mean of 3.8 and standard deviation of 1.0. The
standard error of the difference in means is
(A) 0.766
(B) 0.543
(C) 0.197
(D) 0.295
15. You read that SAT scores in high school explain only 9% of the variation in student’s later grades in college. The correlation between
SAT scores and college grades is therefore:
(A) r = 0.9
(B) r = 0.81
(C) r = 0.09
(D) r = 0.3
(E) r = 0.03
16. Which of the following is equal in a normal distribution?
I. Mean
II. Median
II. Mode
(A) I and II only (B) I and III only (C) II and III only
(D) I, II, and III
(E) none of the above
17. Which of the following statement(s) is true?
(A) Two normal curves can have the same mean, but different standard deviations.
(B) If a data set is normally distributed, approximately 68% of the data is within one standard deviation of the mean.
(C) The standard normal distribution has a mean of 0 and a standard deviation of 1.
(D) The area under every normal curve is 1, no matter what the mean or standard deviations
(E) All of the above.
18. Which of the following would you expect to be true about the correlation between distances and the total tolls paid on the Sam
Houston Tollway
(A) Strong and positive
(B) Weak and positive
(C) Zero
(D) Strong and negative
(E) Weak and negative
19. Gender is a _________ variable and weight is a ___________ variable.
(A) Quantitative; categorical
(B) Categorical; quantitative
(C) Explanatory; response
(D) Response; explanatory
(E) None of the above
20. The standard error of the sample mean is determined by:
(A) Size of the population
(B) Size of the sample
(D) Number of samples
(E) None of the above
21. Which of the following events are NOT disjoint?
(A) Drawing a red card that’s a spade.
(C) Drawing a king that’s a queen
(C) Sample proportion
(B) Rolling an even number that’s prime
(D) None of the above.
22. Which has a larger probability?
I. Picking a red card or a king in one draw
II. Rolling a 7 or better on two dice
(A) I
(B) II
(C) They are the same
23. Suppose a study finds that the correlation coefficient relating family income to SAT scores is
r = 0.89. Which of the following conclusions are justified?
I. Poverty cause low SAT scores
II. Wealth causes high SAT scores
III. There is a strong association between family income and SAT scores.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I, II, and III
24. Nancy and Connie both took the ABC achievement test, which has N (950, 50). If Nancy scored 2.5 standard deviations above the
mean and Connie had a score of 675, how much higher was Nancy’s score?
(A) 1075
(B) 1700
(C) 400
(D) 525
(E) none of these are correct
25. A certain test has a mean of 60 and a standard deviation of 15. To convert the scores to a different scale, the test makers use the
following transformations: x* = 40 + 0.8 x. What is the new mean and new standard deviation?
(A) 88 ; 52
(B) 48 ; 12
(C) 48; 52
(D) 88; 12
(E) none of the above
26. Individual observations that fall well outside the overall pattern of the data are called:
(A) symmetric
(B) outliers
(C) gaps
(D) skewed
(E) normal
27. A distribution is ____________ if the portions greater and less than its center are mirror images of each other.
(A) skewed right
(B) reflected
(C) truncated
(D) skewed left
(E) symmetric
28. Which of the following is not a criteria for a Student T-test?
(A) A simple random sample
(B) The sample standard deviation
(C) No outliers in the distribution (D) A sample less than 30
29. A Student t-distribution has a standard error of 0.52, a sample size of 92, and a mean of 37. What is the standard deviation?
(A) 0.0542
(B) 0.1405
(C) 0.026
(D) 4.99
30. Which of the following does not have to be true for binomial probabilities?
(A) A fixed number of trials
(B) The “n” observations are all independent.
(C) Each observation has 2 possible outcomes.
(D) n > 30
(E) The possibility for each outcome is fixed.
31. Suppose you roll a six-sided die 10 times. What is the probability of getting three 5’s in those 10 rolls?
(A) 0.60
(B) 0.30
(C) 0.000618
(D) 0.155
(E) 0.930
32. A study of department chairperson ratings and student ratings of the performance of high school statistics reports a correlation of r =
1.14 between the two ratings. From this information we can conclude that
(A) Chairpersons and students tend to agree on who is a good teacher
(B) Chairpersons and students tend to disagree on who is a good teacher
(C) There is a little relationship between chairperson and student ratings of teachers
(D) There is a strong association between chairperson and student ratings of teachers, but it would be incorrect to infer causation.
(E) a mistake in arithmetic has been made.
33. The heights of American men age 18 to 24 are approximately normally distributed with mean 68 inches and standard deviation 2.5
inches. Only about 5% of young men have heights outside the range of:
(A) 65,5 inches to 70.5 inches (B) 63 inches to 73 inches
(C) 60.5 inches to 75.5 inches
(D) 58 inches to 78 inches
34. The scores on a statistics exam are strongly skewed to the left. What is the best way to describe the distribution?
(A) The five number summary
(B) The mean and standard deviation
(C) The mean, median, and mode (D) The correlation and its square.
35. You record the age, marital status, and earned income of a sample of 1363 women. What is the number of variables you have
recorded?
(A) 1363
(B) four- age, marital status, income, and number of women
(C) three- age, marital status, and income.
(D) two- age and income (marital status is not a variable because it is not a quantitative data)
36. Other things being held equal, the margin of error in a confidence interval decreases as:
(A) The confidence level increases
(B) The sample size, n, increases.
(C) The population standard deviation increases.
(D) The sample size, n, decreases.
(E) The sample mean decreases.
37. In hypothesis testing, a p-value of less than 5% indicates the following:
(A) The p-value is statistically significant.
(B) One would fail to accept Ho, the status quo.
(C) A test statistic is large (greater than 1.9) to give such a small p-value.
(D) One would support the claim of change, Ha
(E) All of the above
38. A copy machine dealer has data on the number “x” of copy machines of each of 89 customer locations and the number “y” of service
calls in a month at each location. Summary calculations give
x = 8.4
sx = 2.1
sy = 3.8
r = 0.86
y = 14.2
What is the slope of the least squares regression line of the number of service calls on the number of copies?
(A) 0.86
(B) 1.56
(C) 0.48
(D) none of these
(E) Cannot determine from the information given.
39. A company employs over 5000 workers of whom 20% are Hispanic. If the 20 members of the union executive committee were chosen
form the workers, without regard to ethnic background, the number of Hispanics on the committee would have the B ( 20, 0.2)
distribution. What is the probability that 4 or fewer members of the committee are Hispanic?
(A) 0.6296
(B) 0.3819
(C) 0.6181
(D) 0.3704
(E) 0.3999
40. A professor teaches two statistics classes. The morning class has 25 students and their average on the first test was 82. The evening
class has 15 students and their average on the same test was 74. What is the average on this test if the professor combines the sores for
both classes?
(A) 76
(B) 78
(C) 79
(D) 80
(E) The average cannot be calculated since individual scores of each student are not available.
41. The histogram below displays a set of measurements.
Which of the boxplots below displays the same set of measurements?
(a) A (b) B
(c) C
(d) D (e) E
42. A random sample of size 10 was taken from a population. The sample has a variance of zero. Which of the following statements must
be true?
I. The population also ahs a variance of zero.
II. The sample mean is equal to the sample median.
III. The ten data points in the sample are equal in numerical value.
(A) I only
(B) II only
(C) III only
(D) I and II
(E) II and III
Y P(Y=y)
X P(X =x)
1
1/6
2
2/3
3
?
1
?
2 1/4
3 1/4
4
?
43. The tables above show part of the probability distribution for random variables X and Y. If X and Y are independent and the joint
probability P ( X = 3, Y = 4) =
(A) 1/8
(B) 1/6
1
then P( Y= 1) equals:
16
(C) 1/4
(D) 3/8
(E) 1/2
44. For college-bound high school seniors in 1996, the nationwide mean SAT verbal score was 505 with a standard deviation of about
110, and the mean SAT math score was 508 with a standard deviation of about 110. Students who do well on the verbal portion of the
SAT tend to do well on the mathematics portion. If the two scores from each student are added, then mean of the combined scores is
1,013. What is the standard deviation of the combined verbal and math scores?
(A)
110
2
(B) 110
(C)
1102  1102
(D) 220
(E) The standard deviation cannot be computed from the information given
45. As shown above, the least-squares regression line has been fitted to the winning percentages for a local sports team in each of the
years 1983 through 1995. The percentage for the 1996 season was then plotted (as circled above). Which of the following statements
correctly describes how the value for the 1996 season will change the appearance of the least-squares regression line and the correlation
coefficient if a new least-squares regression line is fitted to the 1983 through 1996 data?
(A) The 1996 point will make the LSQR line steeper and the correlation coefficient stronger.
(B) The 1996 point will make the LSQR line steeper and the correlation coefficient weaker.
(C) The 1996 point will make the LSQR line closer to horizontal and the correlation coefficient stronger.
(D) The 1996 point will make the LSQR line closer to horizontal and the correlation coefficient weaker.
(E) The 1996 point will not have any effect on the LSQR line since it follows the same downward trend.
46. A random sample of two observations is taken from a population that is normally distributed with a mean of 100 and a standard
deviation of 5. Which of the following is closest to the probability that the sum of the two observations is greater than 221?
(A) 0.0015
(B) 0.0250
(C)0.0500
(D) 0.4500
(E) 0.9985
47. A particular psychologist test is used to measure academic motivation. The average test score for all female college students
nationwide is 115. A large university estimates the mean test score for female students on its campus by testing a random sample of “n”
female students and constructing a confidence interval based on their scores.
Which of the following statements about the confidence interval are true?
I. The resulting interval will contain 115.
II. The 95% confidence interval for n = 100 will generally be shorter than the 95% confidence interval for n= 50.
III. For n=100, the 95% confidence interval will be longer than the 90% confidence interval.
(A) I only
(B) II only
(C) III only
(D) II and III
(E) None of the above gives a complete set of true responses.
48. The primary reason for blocking when designing an experiment is to reduce:
(A) The sensitivity of the experiment (B) Variation
(C) the need for randomization
(D) bias
(E) confounding
49. A survey was conducted at a movie theater to determine movie-goers’ preference for different kinds of popcorn. The results of the
survey showed that Brand A was preferred by 65% of the people with a margin of error plus or minus 3%. What is meant by the statement
“plus or minus 3%”?
(A) Three percent of the population that was surveyed will change their minds.
(B) Three percent of the time the results of such a survey are not accurate.
(C) Three percent of the population was surveyed.
(D) The true proportion of the population who preferred Brand A popcorn could be determined if 3% more of the population was
surveyed.
(E) It would be unlikely to get the observed sample proportion of 65% unless the actual percentage of people in the population of moviegoers who prefer Brand A is between 62% and 68%.
50. When performing a test of significance for a null hypothesis, H0, against the alternative hypothesis, Ha, the p-value is:
(A) the probability that Ho is true.
(B) the probability that Ha is true.
(C) the probability that Ho is false.
(D) the probability of observing a value of a test statistic at least as extreme as that observed in the sample if Ho is true.
(E) the probability of observing a value of a test statistic at least as extreme as that observed in the sample if Ha is true.
51. Twenty men and 20 women with high blood pressure were subjects in an experiment to determine the effectiveness of a new drug in
lowering blood pressure. Ten of the 20 men and 10 of the 20 women were chosen at random to receive the new drug. The remaining 10
men and 10 women received a placebo. The change in blood pressure was measured for each subject. The design of this experiment is:
(A) Completely randomized with one factor, drug.
(B) Completely randomized with one factor
(C) Randomized block, blocked by drug and gender.
(D) Randomized block, blocked by drug
(E) Randomized block, blocked by gender.
52. A large elementary school has 15 classrooms, with 24 children in each classroom. A sample of 30 children is chosen by the following
procedure:
“Each of the 15 teachers selects 2 children from his or her classroom to be in the sample by numbering the children from 1 to 24, then
using a random digit table to select two different random numbers between 01 and 24. The 2 children with those numbers are in the
sample.” Did this procedure give a simple random sample of 30 children from the elementary school?
(A) No, because the teachers were not selected randomly.
(B) No, because not all possible groups of 30 children had the same chance of being chosen.
(C) No, because not all children had the same chance of being chosen.
(D) Yes, because each child had the same chance of being chosen.
(E) Yes, because the numbers were assigned randomly to the children.
53. The corn rootworm is a pest that can cause significant damage to corn, resulting in a reduction in yield and thus in farm income. A
farmer will examine a random sample of plants from a field in order to decide whether or not the number of corn rootworms in the whole
field is at a dangerous level. If the farmer concludes that it is, the field will be treated. The farmer is testing the null hypothesis that the
number of rootworms is not at a dangerous level against the alternative hypothesis that the number is at a dangerous level. Suppose that
the number of corn rootworms in the whole field actually is at a dangerous level.
Which of the following is equal to the power of the test?
(A) The probability that the farmer will decide to treat the fields.
(B) The probability that the farmer will decide not to treat the field.
(C) The probability that the farmer will fail to reject the null hypothesis.
(D) The probability that the farmer will reject the alternative hypothesis.
(E) The probability that the farmer will not get a statistically significant result.
54. A statistics professor is interested in exploring the relationship between student’s grades on the midterm (x) and final exam grades (y).
He calculates that the regression equation is
= 15.29 + 0.96x. What does the 0.96 mean?
(A) 96% of the variation in y is explained by x.
(B) For each additional point on the midterm, the predicted final score would increase by 0.96.
(C) For each additional point on the final, the predicted midterm score would increase by 0.96.
(D) 96% of the variation in x is explained by y.
(E) None of the above
55. Which of the following would give a simple random sample of AHS students?
(A) Randomly picking 20 students from a randomly chosen Spanish class.
(B) Asking the first 20 students who arrive to school.
(C) Writing down the names of students in the library at lunch and then drawing the names of 20 students from a hat.
(D) Randomly asking 5 freshmen, 5 sophomores, 5 juniors, and 5 seniors.
(E) None of the above
56. If every woman married a man who was exactly 2 inches taller than she, what would the correlation between the heights of married
women and men be?
(A) somewhat negative
(B) somewhat positive
(C) 0
(D) 1
(E) – 1
57. If you flip a coin three times, what is the probability that you get at least one head?
(A) 1/8
(B) 3/8
(C) 1/2
(D) 7/8
58. We hypothesize that 90% of female students remain in senior level AP math courses in Texas all
year whereas only 80% of senior male students remain in senior level AP math courses in Texas all year. If
we sampled 40 female students and 30 male students, what would be the standard deviation of the difference
between the sample proportions?
(A) 0.0871 (B) 0.2217 (C) 0.1205
(D) 0.0837
(E) 0.7201
59. Which of the following pairs of events are NOT independent?
(A) Flipping a head, flipping a tail
(B) Rolling a 6 on a die, rolling another 6
(C) Drawing a king, drawing another king (without replacement)
(D) Drawing a king, drawing another king (with replacement)
60. In an attempt to discover if the reaction time to a new pain medicine is different in men and women, Methodist Hospital decided to
conduct a test in which each of the subjects would receive a dosage proportionate to his/her body weight. The results of the men were then
compared to those of the women. This is an example of a __________ experiment.
(A) Matched pair
(B) Blocked
(C) Stratified
(D) Systematic
(E) Cluster
61. Three main principles in experimental design are control, randomization, and ___________.
(A) Matching
(B) Placebo
(C) Comparison of results (D) Replication
62. A social scientist wished to determine the difference s between the percentage of Los Angeles marriages and the percentage of New
York marriages that end in divorce in the first year. How large of a sample (same for each group) should be taken to estimate the
difference to within ±.07 at the 94% confidence level?
(A) 181
(B) 361
(C) 722
(D) 1083
(E) 1443
63. The Law of Large Numbers states that:
(A) In order to have a good experiment; one must have a large sample.
(B) When conducting an experiment, one must work with a large mean.
(C) When conducting an experiment, one must work with a large standard deviation.
(D) In the long run, the observed mean approaches and remains close to the population mean.
(E) In the long run, the sample mean will become larger than the population mean.
64. In a statistics course a least squares regression equation was computed to predict the final score from the score on the first test. The
equation of the LSRL was ŷ = 10 + 0.9x where “y” is the final exam score and “x” is the score on the first exam. If James scored 78 on
the first test and 88 on his final exam, what is the value of the residual at this point?
(A) -7.8
(B) -1.9
(C) -1.3
(D) 1.9
(E) 7.8
65. Data are obtained for a group of college freshmen examining their SAT scores from their senior year of high school and their GPA’s
during their first year in college. The resulting regression equation is ŷ = .00161x +1.35 where r = .632. What percentage of the
variation in GPA’s can be explained by looking at the SAT scores?
(A) 0.16%
(B) 16.1%
(C) 39.9
(D) 63.2%
(E) Cannot be determined from the information given
66. What is the meaning the p-value of a test statistic?
(A) The probability, assuming that Ha is true, that the test statistic will take a value at least as extreme as that actually observed.
(B) The probability, assuming that Ho is true, that the test statistic will take a value at least as extreme as that actually observed.
(C) The probability, assuming that Ha is not true, that the test statistic will take a value at least as extreme as that actually observed.
(D) The probability, assuming that Ho is not true, that the test statistic will take a value at least as extreme as that actually observed
67. Of the following, which p-value would be significant at the 5% level?
(A) 0.51
(B) 0.055
(C) 0.123 (D) all of these answers are significant (E) none of these are significant
68. Given a LSRL with a high r2 value, which of the following are true?
I. It is a risky procedure to predict the y-values within the range of the x-values given by the data.
II. It is a risky procedure to predict the y-values outside the range of x-values given by the data.
III. It is a safe procedure to predict the y-values within the range of the x-values given by the data.
IV. It is a safe procedure to predict the y-values outside the range of x-values given by the data.
(A) I and II only
(B) II and III only
(C) II and IV only
(D) III and IV only
(E) I and IV only
69. Which of the following is a resistant statistic?
(A) mean
(B) standard deviation
(E) median
(C) chi-squared
(D) t-score
70. In a normal distribution, approximately what percent of the observations fall within 3 standard deviations of the mean?
(A) 95%
(B) 98%
(C) 99%
(D) 98.5%
(E) 99.7%
71. In a lottery game, the probability of winning the following amount of money is as follows:
Money($)
5
100
5000
Probability
1/50
1/1000
1/10000
If each ticket costs $1.00, how much can you expect to win?
(A) $0.70
(B) -$0.25
(C) -$0.88
(D) -$0.30
(E) $0.50
72. A two-sample t-test gives a t-value of 4.5. The .05 critical value from the t-table is 3.7. Which of the following is true?
(A) The p-value will be greater than .05
(B) The p-value will be smaller than .05
(C) Either “A” or “B” may be true depending on the sample size
(D) Either “A” or “B” may be true depending on the degrees of freedom.
73. Suppose that 60% of students who take the AP English exam score a 4 or a 5, 25% score a 3, and the rest score a 1 or 2. Suppose
further that 95% of those scoring 4 or 5 receive college credit, 50% of those scoring 3 receive college credit, and 4% of those scoring 1 or
2 receive college credit. A student is chosen at random from among those who took the AP exam and who received college credit. What is
the probability that he/she received a 3 on the exam?
(A) 0.125
(B) 0.178
(C) 0.701
(D) 0.813
(E) 0.822
74. In designing an experiment, blocking is used
(A) To reduce bias
(C) As a substitute for a control group
(E) To reduce variation
(B) To control the level of the experiment
(D) As the first step in randomization
75. In testing: H o : 1   2  0 and H a : 1   2  0 ,a two-sample t-test gives a p-value of .042. Which of the following are true?
(A) The null hypothesis of no difference cannot be rejected at the 0.05 significance level.
(B) The 90% confidence interval contains the value 0 in its interior.
(C) The null hypothesis of no difference can be rejected at the 0.05 significance level.
(D) The 95% confidence interval contains the value 0 in its interior.
76. Which of the following would be a good reason to use a z-test instead of a t-test as a test statistic?
(A) The sample size is large
(B) The variances are assumed to be equal.
(C) The degree of freedom is greater than 15.
(D) The standard deviation of the population is known.
(E) None of these
77. When comparing two samples which of the following is the most important?
(A) The samples are selected randomly
(B) The sample sizes are equal
(C) The samples have the same variances
(D) The samples come from approximately normal distributions
(E) There are no outliers in the data
78. Which of the following assumptions is the t-test LEAST robust against?
(A) Small sample size
(B) Outliers
(C) Non-symmetric distribution of the data
(D) Transformed data
The heart disease death rates per 100,000 people in the United States for certain years, as reported by the National Center for Health
Statistics, were
Year
1950
1960
1970
1975
1980
Death Rate
307.6
286.2
253.6
217.8
202.0
79. Which of the following is a correct interpretation of the slope of the least squares regression line for the data above?
A) The heart disease rate per 100,000 people has been dropping about 3.627 per year
B) The baseline heart disease rate is 7386.87
C) The regression line explains 96.28% of the variation in heart disease death rates over the years.
D) The regression line explains 98.12% of the variation in heart disease death rates over the years.
E) Heart disease will be cured in the year 2036.
80. Based on the regression line, what is the predicted death rate for the year 1983?
(A) 195.4 per 100,000 people
(B) 192.5 per 100,000 people
(C) 196.8 per 100,000 people
(D) 198.5 per 100,000 people
(E) 194.5 per 100,000 people
81. In making predictions about the data from a regression equation, it is often dangerous to make predictions about data outside the
domain of the explanatory variable. The term for this process is called_______.
(A) interpretation
(B) interpolation
(C) extrapolation
(D) estimation
82. Amos Tversky and Thomas Gilovich in their study on the “Hot Hand” in basketball (Chance, Winter 2989, page 20), found that in a
random sample of games, Larry Bird hit a second free throw in 48 of 53 attempts after the first free throw was missed. Larry hit a second
free throw in 251 of 285 attempts after the first free throw was made. Is there sufficient evidence to say that the probability that bird will
make a second free throw is different depending on whether or not he made the first free throw?
(A) Since p < .001 , there is sufficient evidence that the probability that Larry Bird will make a second free throw is different
depending on whether he made the first free throw or not.
(B) Since .001 < p < .01, there is sufficient evidence that the probability that Larry Bird will make a second free throw is different
depending on whether he made the first free throw or not.
(C) Since .01 < p < .05, there is sufficient evidence that the probability that Larry Bird will make a second free throw is different
depending on whether he made the first free throw or not.
(D) Since .05 < p < .10, there is little evidence that the probability that Larry Bird will make a second free throw is different
depending on whether he made the first free throw or not.
(E) Since p > .10, there is little evidence that the probability that Larry Bird will make a second free throw is different depending on
whether he made the first free throw or not.
83. A study of accident records at a large engineering company in England (The Lancet, October 22, 1994) reported the following number
of injuries on each shift for 1 year:
Shift
Morning
Afternoon
Night
Number of injuries
1372
1578
1686
Did the study provide enough evidence to say that the number of accidents on the three shifts is not the same?
(A) There is sufficient evidence to say that the number of accidents on each shift is not the same
(B) There is not sufficient evidence to say that the number of accidents on each shift is not the same.
84. An inspection procedure at a manufacturing plant involves picking three items at random and then accepting the whole lot if at least
two of the three items are in perfect condition. If in reality 90% of the whole lot are perfect, what is the probability that the lot will be
accepted?
(A) 0.003
(B) 0.028
(C) 0.081
(D) 0.810
(E) 0.972
500 people used a home test for HIV and then all underwent more conclusive hospital testing. The accuracy of the home test was
evidenced in the following table:
HIV
Healthy
Positive Test
35
25
Negative Test
5
435
85. What is the predictive value of the test? That is, what is the probability that a person tested has HIV and tests positive?
(A) 0.070
(B) 0.130
(C) 0.538
(D) 0.583
(E) 0.875
86. What is the false-positive rate? That is, what is the probability of testing positive given that the person does not have HIV?
(A) 0.054
(B) 0.050
(C) 0.130
(D) 0.417
(E) 0.875
87. What is the sensitivity of the test? That is, what is the probability of testing positive given that the person has HIV?
(A) 0.070
(B) 0.130
(C) 0.538
(D) 0.583
(E) 0.875
88. What is the specificity of the test? That is, what is the probability of testing negative given that the person does not have HIV?
(A) 0.125
(B) 0.583
(C) 0.870
(D) 0.946
(E) 0.950
89. Which of the following are important in the design of experiments?
I. Control of confounding variables
II. Randomization in assigning subjects to different treatments.
III. Replication of the experiment using sufficient numbers of subjects.
(A) I and II only
(B) I and III only
(C) II and III only
(D) I, II, and III (E) None of the above
90. Suppose that 35% of all business executives are willing to switch companies if offered a higher salary. If a job placement service
randomly contacts 100 executives, what is the probability that over 40% will be willing to switch companies if offered a higher salary?
(A) 0.1250
(B) 0.1977
(C) 0.4207
(D) 0.8023
(E) 0.8531
91. If we reject the null hypothesis, when in fact, the null hypothesis is true, we have:
(A) Committed a Type I error (B) Committed a Type II error
(C) A probability of being correct which is equal to the p-value
(D) Explained the power of a test.
92. A researcher plans to conduct a test of hypotheses at the 1% significance level. She designs her study to have power of 0.90 at a
particular alternative value of the parameter of interest. The probability that the researcher will commit a type I error is:
(A) 0.01
(B) 0.10
(C) 0.90
(D) equal to the p-value and cannot be determined until the data is collected
93. The power of a statistical test of hypotheses is:
(A) The smallest significance level at which the data will allow you to reject the null hypothesis.
(B) Equal to one minus the p-value.
(C) The extent to which the test will reject both a one-sided and two-sided hypothesis.
(D) The probability, that at a fixed level, a significance test will reject the null hypothesis when this particular alternative value of the
parameter is true.
94. A manufacturer knows 4% of all floppy disks that come off the production line are defective. What is the probability that if you
randomly select floppy disks from a week of production that you will need to sample 15 disks before you find a defective one?
(A) 0.0226
(B) 0.4579
(C) 0.4353
(D) 0.5421
(E) 0.9774
95. In general, how does tripling the sample size change the confidence interval?
(A) It triples the interval size
(B) It divides the interval size by 3.
(C) It multiplies the interval size by 1.732
(D) It divides the interval by 1.732 (E) This question cannot be answered without knowing the sample size.
96. Pamela is playing an instant lottery game. What is the probability that she will not win until the 8th try if the probability is one out of
100 on a single try?
(A) 0.0009
(B) 0.0093
(C) 0.0993
(D) 0.9321
(E) 0.9907
97. Which of the following are true?
I. In a block design, the random assignment of units to treatments is carried out separately within each block.
II. The purpose of blocking is to reduce variation in results.
III. Matched pairs design is a special type of blocked design.
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
98. The regression line for a set of data is ŷ = 2x + b. this line passes through the point (3 ,4). If x and y are the sample means of the x
and y values respectively, then y 
(A) x
(B) x  3
(C) x  4
(D) 2x  2
(E) 2 x  10
99. If the probability that switch works properly is 0.8, what is the probability that exactly 3 out of 10 switches are defective?
(A) 0.0008
(B) 0.1147 (C) 0.2013
(D) 0.2563
(E) 0.5000
100. Assuming σ is known, which of the following would most likely result in the widest confidence interval for estimating μ.
(A) Large sample size, α = 0.01
(B) Large sample size, α = 0.05
(C) Small sample size, α = 0.01
(D) Small sample size, α = 0.05
(E) Without the sample mean, this question cannot be answered.