AP Statistics Practice Exam

Statistics Independent Study Page 1 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet Multiple-Choice Multiple-Choice Section

Choose the one best answer for each of the following questions.

1. The probability of of getting a specific grade grade in freshman English English is given in the table below. Each letter grade has a specific number of grade points associated with it. What is the GPA (grade point average) in freshman English? Grade Grade Points Probability A.

2.0

B.

2.1

C.

1.9

A

B

C

D

F

4

3

2

1

0

.05

.3

.3

.2

.15

D. 1.8 E.

2.25

2. A 99% confidence interval for the proportion of voters who favor a ballot initiative to lower property taxes is (.68, .76). Which of the following statements are true? I. The probability probability is .99 .99 that between 68% and and 76% 76% of voters will vote to lower property taxes. II. The procedure procedure used to generate this this interval will contain contain the true true population proportion proportion 99% of the time. III. About 99% of those responding are in favor of lowering property taxes. A.

I only

B.

II only

C.

III only

D. I and II only E.

II and III only

_____________ ___________ __ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc.

Statistics Independent Study Page 2 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet 3. A baseball player wants to be among the top 10% of batters in the league based on his batting average. The averages for all players in the league are normally distributed with a mean of .265 and a standard deviation of .023. What is the lowest batting average the player can have and still be among the top 10% of batters? A.

.300

B.

.288

C.

.294

D. .290 E.

.304

4. Which of the graphs below could represent a cumulative frequency plot? B.

A.

D.

C.

E.

5. Which of the following is not an important consideration in experimental design? A.

Randomization to control for bias between groups

B.

Using blocks when experimental units are known to be similar i n some way

C.

Control of treatments to avoid the effects of confounding variables

D. Using observational studies rather than experiments when appropriate E.

Replication on a sufficient number of subjects to control for variation

_____________ © Copyright 2000 Apex Learning Inc. All rights reserved. This material is intended for the exclusive use of registered users only. No portion of these materials may be reproduced or redistributed in any form without the express written permission of Apex Learning Inc.

Statistics Independent Study Page 3 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet 6. A standard deck of 52 cards has 26 red cards and 26 black cards. It has 13 each of Diamonds, Hearts, Clubs, and Spades, and 4 (one of each suit) of Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. Suppose you draw one card at random from a standard deck. Let A = an Ace is drawn. Let D = a Diamond is drawn. Let F = a 10, Jack, Queen, King, or Ace is drawn. Which of the following pairs of events are independent? I. A, D II. A, F III. D, F A.

I only

B.

II only

C.

III only

D. I and III only E.

II and III only

7. An advertisement for a weight loss clinic claims that people who go through the complete program lose an average of 75 lb. A statistician finds that, at the .05 level of significance, if the true weight loss is actually equal to 71 lb, then the power against the claim of 75 lb is .80. Which of the following statements best explains what this means? A.

The probability that the true mean weight loss is 71 lb or less is .8.

B.

If the true average weight loss is 71 lb, the probability of rejecting the claim that it is 75 is .80.

C.

There is a .05 chance of getting a value as deviant as 71 if the true mean weight loss is really 75 lb.

D. There is a .8 chance of rejecting the claim that the true mean weight loss is 75

lb if a sample value of 71 lb is obtained. E.

If the true mean weight loss is 71 lb, the probability of getting a finding as large as 75 lb is .80.

8. You have constructed a 95% confidence interval for a population mean based on a sample size of 15. You find that it is too wide for your purposes. You want to have a 95% interval for the mean, but one that is only half as wide as the one you have. What sample size do you need? A.

15

B.

60

C.

30

D. 45 E.

225


Statistics Independent Study Page 4 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet 9. Which of the following statements are true? I. A stemplot can be thought of as a histogram where you actually see the data. II. A boxplot is an effective way of viewing mean-based measurements. III. A histogram can be constructed using either frequencies or relative frequencies. A.

I only

B.

II only

C.

II and III only


III only

10. A researcher is interested in assessing the effects of jogging on stress reduction. He identifies 25 people who jog regularly and 25 who may exercise in other ways but do not jog. The researcher interviews each of the 50 people to determine their reactions to stress. The 50 subjects did not know they were part of a study. Which of the following statements is true? A.

This is an observational study.

B.

This is a matched pairs experiment.

C.

This is a double-blind study.

D. This is a randomized comparative study. E.

This is survey research based on available data.

11. A sample of the ages of the teachers at a local high school is composed of the following values: 34, 35, 32, 38, 45, 56, 42, 35, 44, 47. You want to use these data to generate a 90% confidence interval for the population mean. What is the upper critical t value (t *) you would use? A.

1.812

B.

1.372

C.

1.383

D. 1.833 E.

1.860


Statistics Independent Study Page 5 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet 12. A data set has the following five-number summary: {31, 50, 58, 62, 87}. Which of the following pairs of values in this data set would be considered outliers? A.

31, 81

B.

32, 81

C.

31, 80

D. 32, 80 E.

33, 86

13. In the game of Chuck-a-Luck, you select a number between 1 and 6, then roll three dice. You win 1 point for each die showing your number. You lose a point only if your number fails to come up on any of the three dice. Thus, in a single turn, you can win 1, 2, or 3 points, or you can lose 1 point. What is the probability that you will win at least 1 point in a single turn? A.

75/216

B.

3/4

C.

1/4

D. 125/216 E.

91/216

14. To select three rats from a group of ten, you decide to use the following set gathered from a table of random numbers: 11793 20495 05907 11384 44982 20751 27498. The rats, named Al, Betty, Chuck, Diane, Ernie, Fran, Guy, Helen, Ira, and Jean, are numbered 1 to 10, respectively. If you started from the left of your number set, which of these groups of rats would you select? A.

117

B.

Al, Al, Guy

C.

Al, Guy, Ira

D. Betty, Helen, Jean E.

Helen, Ira, Diane


Statistics Independent Study Page 6 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet 15. You are testing the hypothesis H 0 : p = .25, and wish to construct a 95% confidence interval for the true population proportion (to see if it contains .25). What is the minimum number of people you will need to interview to have a margin of error no greater than .05? A.

289

B.

385

C.

256

D. 384 E.

1,537

16. You survey a random sample of 75 teenagers to determine whether they prefer to buy CDs or cassettes. You find that 50 of the teenagers say they prefer CDs. You perform a significance test of the hypothesis that the population proportion of those who prefer CDs is .6 ( H 0 : p = .6). For this test, what is SE ˆ? p A.

.0029

B.

.054

C.

.049

D. .057 E.

.544

17. The following regression equation is used to predict College GPA based on High School GPA: College GPA = –.29 + .98(High School GPA). The residual when the High School GPA is 3.1 is .052. What is the actual value of the College GPA when the High School GPA equals 3.1? A.

2.6

B.

2.9

C.

3.0

D. 2.7 E.

2.8


Statistics Independent Study Page 7 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet 18. Chris, Duane and Carl have a free-throw contest. Normally, Chris has an 80% chance of making a free throw, Duane has a 70% chance, and Carl has a 60% chance. Assuming that these probabilities are independent, what are the probabilities that all three make their first shot, and that all three miss their first shot? A.

.336; .024

B.

.336; .128

C.

.336; .664

D. .664; .024 E.

.664; .128

19. Which of the following statements about r , the correlation coefficient , are true? I. Given a set of data ( x i , y i ), the correlation coefficient is the same as the data set we would get if we reversed each x and y value. II. Consider a bivariate data set ( x i , y i ), and a corresponding data set, ( z x i , z y i ), made up of the z -scores of the original data. For the set ( z x i , z y i ), r = the slope of the regression line. III. r 2 represents the proportion of the variation in the dependent variable explained by the regression on the independent variable. A.

I only

B.

II only

C.

III only


I, II, and III

20. Consider the discrete probability distribution shown below. What is X Probability

A.

2

B.

2.24

C.

1.55

0

.17

1

2

3

4

.30

.21

.08

µ X ?

D. 2.08 E.

1.79


Statistics Independent Study Page 8 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet 21. Researchers conduct a clinical trial on a new headache medicine. Fifty subjects are each randomly assigned to one of two groups. One of the groups unknowingly receives the experimental medication and one receives a placebo. The researcher notes that the group receiving the placebo experiences significant relief from headaches. Which of the following are true? I. The new medication has been shown to be ineffective in the treatment of headaches. II. This is an example of the placebo effect : Improvement might be observed even in the absence of any real treatment. III. Since the placebo is effective in treating headaches, doctors should prescribe it rather than a drug that might have potentially serious side effects. A.

I only

B.

II only

C.

III only

D. II and III only E.

I and II only

22. You construct a confidence interval for the difference between two population means. Which of the following statements are true? I. Unless we are justified in pooling our estimates of the population variance, this distribution is only approximated by a t distribution. II. Unlike procedures for a single mean, which require t procedures, z -procedures are usually appropriate for the difference between two means. III. If there is some third variable that exerts an explanatory influence on both variables whose means are being estimated, we are dealing with one-sample rather than two-sample procedures. A.

I only

B.

II only

C.

III only


II and III only


Statistics Independent Study Page 9 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet 23. A data set is found to have a mean of 18 and a standard deviation of 4. The data set is transformed by the linear transformation x* = .5 x + 3. That is, each term in the set is first multiplied by .5 and then has 3 added to the result. The mean and standard deviation, respectively, of the transformed data set are: A.

12; 2

B.

12; 5

C.

12; 7

D. 9; 2 E.

9; 5

24. Which of the following statements are correct? I. A random variable is a numerical outcome of a random phenomenon. II. A density curve lies on or above the horizontal axis, and has an area of 1 under the curve and above the axis. III. If two independent random variables X and Y are combined, σ X + Y =

A.

I only

B.

II only

C.

III only

σ

2

X

+ σ

2

Y

.


I, II, and III


Statistics Independent Study Page 10 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet 25. You are interested in learning how many of the teachers and students at your school would support a constitutional amendment prohibiting flagburning. You obtain a simple random sample of students and teachers at your school and ask the following question: "Since many people have died in support of our flag, do you think flag-burning should be prohibited?" Which of the following is most likely true? A.

The sample proportion agreeing with the statement would probably be less than the true population proportion supporting the amendment.

B.

Within normal limits of variation, the sample proportion agreeing with the statement would probably be very close to the true population proportion supporting the amendment.

C.

The sample proportion agreeing with the statement would probably be greater than the true population proportion supporting the amendment.

D. This question suffers primarily from interviewer bias  the responses will be

biased based on the gender of the interviewer. E.

Since the sample size is not specified, it is not possible to predict the direction of bias, if any.

26. Farley's score on his first statistics test of the year was 58. The scores for the entire class were normally distributed with a mean of 65 and a standard deviation of 5. His score on the second statistics test of the year was 70, but this was an easier test and the class average was 78 with a standard deviation of 6. Which of the following statements is true? A.

Farley is improving in relation to the rest of the class because his score went up.

B.

Farley appears to be improving in relation to the rest of the class because he was not as far below the class average.

C.

Farley did better on the first test because his z -score was greater.

D. Farley did better on the first test because he was not as far away from the class

average. E.

In relation to the rest of the class, Farley did equall y well on both tests.

27. You conduct a

χ

2

test of independence to see if voting preference is related

to ethnicity. You categorize respondents from five different ethnic groups into four different political preference groups. When the analysis is complete, you get a X 2 of 25.27. The P -value for this test is: A.

.15 < p < .20

B.

.10 < p < .15

C.

.05 < p < .10

D. .02 < p < .025 E.

.01 < p < .02


Statistics Independent Study Page 11 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet 28. You want to play a new game that involves rolling a six-sided die. You win if you roll an odd number and lose if you roll an even number. The probability of each number coming up is shown in the table. Given that you win rather than lose, what is the probability that you rolled a 3? Number Probability

A.

.333

B.

.15

C.

.265

1

2

3

4

5

6

.1

.1

.15

.20

.20

.25

D. .122 E.

.58

29. You are designing a survey and plan to draw a simple random sample from a well-defined population, but are worried that the sample you have in mind might have more variability than you want. Which of the following would help control for the amount of variability in the sample? I. Increase the sample size. II. Stratify your sample to make sure each group of interest is proportionately represented. III. Simplify the wording of the questions in your survey. A.

I only

B.

I and II only

C.

II only

D. II and III only E.

I, II, and III


Statistics Independent Study Page 12 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet 30. Consider the scatterplot shown below. The point marked A is an influential point. If you removed point A and computed a new regression equation, which one of the following would be true?

A.

The correlation would be weaker and the slope of the regression line would be closer to –1.

B.

The correlation would be stronger and the slope of the regression line would be closer to 1.

C.

The correlation would be stronger and the slope of the regression line would be closer to –1.

D. The correlation would be weaker and the slope of the regression line would be

closer to 1. E.

Both the correlation coefficient and the slope of the regression line would be closer to 0.

31. The table shown below gives the observed values for a

χ

2

test of

independence. What is the expected value for the cell in the fourth row, second column (the cell with the "10" in it)? 15 12 18 15 14 A.

11.0

B.

9.8

C.

10.6

8 12 9 10 12

D. 10.2 E.

9.4


Statistics Independent Study Page 13 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet 32. The regression equation for ln y on x for the data shown in the table is given by ln y = .400 + .565 x . What is the residual when x = 4?

A.

11.34

B.

.296

C.

.21

x

y

ln y

1 2 3 4 5 6

2 5 11 14 30 34

.69315 1.60944 2.39790 2.63906 3.40120 3.52636

D. –.296 E.

–.021

33. You find the correlation coefficient between two variables to be –.90. You may conclude that: A.

high values of the explanatory variable are associated with low values of the response variable.

B.

approximately 90% of the variation in the response variable is explained by regression on the explanatory variable.

C.

low values of the explanatory variable are associated with low values of the response variable.

D. a cause-and-effect relationship exists between the explanatory variable and the

response variable, since the correlation is so strong. E.

high values of the explanatory variable are associated with high values of the response variable.

34. Which of the following is not a probability sample? A.

Simple random sample

B.

Stratified random sample

C.

Systematic sample

D. Judgement sample E.

None of these are probability samples


Statistics Independent Study Page 14 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet 35. Given that the computations in the output shown here were based on 12 ordered pairs, what is a 99% confidence interval for the slope of the regression line?

Regression Analysis

The regression equation is Value = – Age Predictor Constant Age s = 1.451

Coef 34.6795 –4.2179 R-sq = 97.1%

A.

–4.22 ± 3.169(.232)

B.

–4.22 ± 3.103(.232)

C.

–4.22 ± 3.169(1.451)

Stdev 0.9150 0.2324

t-ratio 37.90 –18.15

p 0.000 0.000

R-sq(adj) = 96.8%

D. –4.22 ± 3.103(1.451) E.

34.68 ± 3.169(.232)

36. Referring to the computer output shown here, which of the following statements are true? I. The standard error of the slope of the regression line is .2324. II. There appears to be a statistically significant relationship between "Age" and "Value." III. The standard error of the residuals is 1.451.

Regression Analysis

The regression equation is Value = – Age Predictor Constant Age s = 1.451 A.

I only

B.

II only

C.

III only

Coef 34.6795 –4.2179 R-sq = 97.1%

Stdev 0.9150 0.2324

t-ratio 37.90 –18.15

p 0.000 0.000

R-sq(adj) = 96.8%


I, II, and III


Statistics Independent Study Page 15 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet 37. A random variable X has

σ X =

6. Each term in the distribution is

transformed by x* = 3 + 6 x . What is the value of

σ

2

X *

? (That is, what is the

variance of the new distribution?) A.

36

B.

6

C.

1,296

D. 216 E.

144

38. You roll two dice, A and B. What is the probability that both dice show the same number given that one of the dice shows a 3 or larger? (Use the table shown here to help you find your answer.) B1 A1

A2 A3 A4 A5 A6

A.

8/9

B.

1/8

C.

1/9

(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6 ,1)

B2

(1, (2, (3, (4, (5, (6,

2) 2) 2) 2) 2) 2)

B3

(1, (2, (3, (4, (5, (6,

3) 3) 3) 3) 3) 3)

B4

(1, (2, (3, (4, (5, (6,

4) 4) 4) 4) 4) 4)

B5

(1, (2, (3, (4, (5, (6,

5) 5) 5) 5) 5) 5)

B6

(1, (2, (3, (4, (5, (6,

6) 6) 6) 6) 6) 6)

D. 1/16 E.

1/4


Statistics Independent Study Page 16 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet 39. You roll two dice, A and B. Given that at least one of the dice shows a 5, what is the probability that die A shows a 5? (Use the table below to help you find your answer.) B1 A1 A2 A3 A4 A5 A6

A.

11/36

B.

1/6

C.

1/11

(1, (2, (3, (4, (5, (6,

1) 1) 1) 1) 1) 1)

B2

(1, (2, (3, (4, (5, (6,

2) 2) 2) 2) 2) 2)

B3

(1, (2, (3, (4, (5, (6,

3) 3) 3) 3) 3) 3)

B4

(1, (2, (3, (4, (5, (6,

4) 4) 4) 4) 4) 4)

B5

(1, (2, (3, (4, (5, (6,

5) 5) 5) 5) 5) 5)

B6

(1, (2, (3, (4, (5, (6,

6) 6) 6) 6) 6) 6)

D. 6/11 E.

1/2

40. You collect data on two independent random samples from normal populations. You conduct a two-sided hypothesis test and pool the estimates of the population variance. The data are: x 1 = 17.5, s x 1 = 1.33, n1 = 28, x 2 = 18.2, s x 2 = 1.48, n2 = 30, s p = 1.40, s x 1 − x 2 = .37. What is

the value of t for this test and what is the corresponding P -value? A.

–1.90; .025 < p < .05

B.

–.5; p > .25

C.

–1.90; .05 < p < .10

D. –1.76; .025 < p < .05 E.

–2.05; .04 < p < .05


Statistics Independent Study Page 17 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet Free-Response Section Introduction

These questions simulate the Free-Response section of the AP Exam. Questions 1-5 should take about 10-15 minutes each. Question 6 is an "Investigative Task," and should take about 20-30 minutes. You should do all that you can do in no more than 90 minutes. 1. Prospective lawyers must pass the bar exam before they can practice law. They do

not all pass it the first time. A group of 75 practicing lawyers were asked how many times they had to take the bar exam before they passed. The results were as follows: Times Attempted Number of Lawyers A.

1

2

3

4

5

6

7

40

12

8

9

5

0

1

Construct a cumulative relative frequency plot of these data on the graph below:

C U M R E L F R E Q

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

1

2

3

4

5

6

7

NUMBER OF ATTEMPTS

B.

What are the mean and median number of attempts needed to pass the bar for these 75 lawyers?

2. As research director for a drug company, you want to determine the effectiveness of

a new treatment for arthritis. You suspect that the drug might have different effects at different treatment levels (the levels under consideration are 350 mg and 500 mg). You also suspect that men and women might react differently to the medication, and that people 60 and over might experience different effects than those under 60. You have available to you 180 volunteers who suffer from arthritis. Exactly half of these volunteers are men and half are women, and exactly half of the volunteers are 60 years old or older. A.

Is blocking needed to create the best possible experimental design in this case? If yes, what would the blocks be and why? If not, why not?


Statistics Independent Study Page 18 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet B. C.

Describe the design of an experiment to measure the effectiveness of this new drug. Include elements from your answer to part A as needed. Suppose your research team had developed a 1-10 scale for arthritis relief to determine whether real differences existed between treatment levels. Thinking only in terms of 350 mg vs. 500 mg dosages (that is, do not consider the placebo responses here), describe the method of analysis you would use to support your findings.

3. Researchers conduct a program to improve the mathematical skill of noncollege math majors of 12 volunteers. The math skills of the volunteers are evaluated before and after the training. The results are as follows: Subject Archie Betty Chuck Dolores Eddie Fran George Helen Irving Janice Ken Loretta

Pre-test 56 63 72 59 58 65 61 74 52 60 60 79

Post-test 58 62 75 61 57 69 63 74 54 58 64 80

Does this provide evidence that the program was effective in improving mathematics skill for these subjects? Use good statistical reasoning in your answer.

4. The California State Lottery "Pick 6" game allows you to pick six di fferent numbers

from 1 through 51. A machine randomly picks six different numbers from 1 through 51 (once a number is chosen, it is not returned to the box and cannot be chosen again). You can win money if you match at l east 3 of the numbers. Let X = the amount of numbers that you match. A. What is P ( X = 6)? That is, what is the probability that you match all six numbers? Provide an understandable explanation. B. Consider a variation of this game in which each number could be repeated. That is, once a ball is drawn with a number on it, it is returned to the box and can be drawn again. What is the probability that you will get at least one match in the first 5 drawings? C. What is the probability that the first match comes on the fifth drawing?


Statistics Independent Study Page 19 of 19 Mixed Practice with Multiple-Choice and Free-Response Questions Study Sheet 5. Over the years, approximately 60% of the students that have attempted the AP

Statistics Exam have passed with a grade of 3 or higher out of a possible 5. Smart Academy, a prestigious private school, believes its students do better on the Exam, on average. This year, Smart Academy had 36 students take the AP Statistics Exam. For some reason, the school has scores for only 35 students—one score is missing. Of these students, 26 received a grade of 3 or better. You are hired to advise the administration as to whether they should claim in their advertising that their students do better than the national average. A. Perform a significance test of the hypothesis H 0 : p = .6 based on the 35 scores received by the school. Use a significance level of .05. B. The missing test turns up under a pile of papers on the Assistant Principal's desk. The administration has already decided to publicize their success rate. If the missing test was discovered before the analysis was done, is it possible that this would have affected the school's decision to publicize their success?

6. In a study, the blood cholesterol levels of 500 American men were recorded and summarized in the table below (data from Primer for the Biomedical Sciences, by O.J. Dunn, NY, Wiley, 1977). The corresponding sample mean and standard deviation were calculated to be 275 and 47, respectively. Do the data provide evidence that the blood cholesterol levels are normally distributed? Use at least one graphical technique for an intuitive argument and one test of significance to support your conclusion. Note: Use of the Empirical Rule is not an acceptable approach in this case. Cholesterol Level Less than 189.5 189.5 – 219.5 219.5 – 249.5 249.5 – 279.5 279.5 – 309.5 309.5 – 339.5 339.5 – 369.5 369.5 – 399.5 Over 399.5

Frequency 17 41 80 134 118 71 24 13 2

TI-83 screens are used with the permission of the publisher. Copyright Instruments, Incorporated.

 1996,

Texas


AP Statistics Practice Exam

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