AP-Statistics Exam

7/23/2019 AP-Statistics Exam

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Statistics Assignment Page 1 of 23Full-Length Practice Exam

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

Multiple-Choice Section (90 minutes)

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

Do notsend your multiple choice answers back to your instructor. Only send your free-response answers (next section) to your instructor.

It's important to stay within the time limit to see how you'd do under real test conditions. Ifyou can't finish all the questions in 90 minutes, go back later and do the problems youweren't able to finish.

1. A five-number summary of a univariate data set is determined to be[10, 15, 25, 45, 85]. These data are to be used to construct a (modified)

boxplot. Which of the following statements are true?

I. The mean is probably greater than the median.

II. There is at least one outlier.

III. The data are skewed to the right.

A. I only

B. II only

C. III only

D. I and III only

E. I, II, and III

2. You have a rather strange die: Three faces are marked with the letterA, twofaces with the letter B, and one face with the letter C. You roll the die until youget a B. What is the probability that the first Bappears on the first or the

second roll?

A. .333

B. .704

C. .556

D. .037

E. .296


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3. You are going to construct a 95% confidence interval for the differencebetween two independent sample means. There are 12 subjects in one sampleand 11 in the other. You think that the two populations have the same standard

deviation, and so decide to use a pooled estimator of the population variance.

How many degrees of freedom would you use for this t procedure?

A. 21

B. 23

C. 10

D. 12

E. 22

4. The regression line for this bivariate data set is xy 17.41.19 += . What is the

residual for the point with anx-value of 68?

x 56 45 68 49 58 63 66 62y 28 25 34 30 32 36 23 29

A. 30.97

B. 3.03

C. 34

D. 30.97

E. 3.03


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5. Which of these distributions has the largest standard deviation? Assume thatthe range is the same for each histogram shown here.

A.

B.

C.

D.

E.


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6. Randomization is important in experiments because:

A. it makes treatment and control groups equal in size.

B. it ensures that there are enough subjects in all treatment groups.

C. it masks the placebo effect.D. it controls for any bias the experimenter may have.

E. it helps ensure that treatment and control groups are as alike as possible.

7. You have a rather strange die: Three faces are marked with the letterA, two

faces with the letter B, and one face with the letter C. If you were to roll this

die, what is the probability that at least one of the first two rolls would be a B?

A. 5/9

B. 1/3

C. 1/9

D. 4/9

E. 7/9

8. You want to see if a coin is fair. You flip it 5 times and count the number ofheads. If His the number of heads obtained in five flips of the coin, what is the

P-value of the test when Hequals 4?

A. 5/32

B. 6/32

C. 7/32

D. 8/32

E. 9/32

9. You are going to construct a 99%t confidence interval for a population meanbased on a sample of size 22. What is the critical value of t(t*) you will use to

construct the interval?

A. 2.819

B. 2.845

C. 2.080

D. 2.831

E. 2.518


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10. Franny is told that thez-score for her SAT test score was 1.2 compared to alltwelfth-grade girls who took the test. Which of the following best describeswhat this means?

A. Only 1.2% of the twelfth-grade girls taking this test had scores higher than Franny.

B. Franny's score is 1.2 points higher than the average score for all twelfth-grade girlswho took the SAT.

C. Franny received 1,200 on the SAT.

D. Franny's score is 1.2 standard deviations above the mean of twelfth-grade girls whotook the SAT.

E. Franny's score is 1.2 times greater than the average score for all twelfth-grade girlswho took the SAT.

11. A double-blindexperimental design is:

A. one in which neither the experimenter nor the subject are aware of which treatmentthe subject receives.

B. one whose purpose is to standardize responses of the various treatment groups.

C. one in which the subject is unaware of whether they are receiving the treatment ornot, but the researcher is aware.

D. one in which groups are matched on a specific set of criteria so as to eliminate anyobvious differences between the groups.

E. another way to describe an experiment in which no placebo is used.

12. Sometimest procedures are referred to as robust. Which of the following bestdescribes what this means?

A. They are not affected by extreme values.

B. They can be used in many different situations, unlike less robust measures.

C. They are still useable even when the assumptions necessary for their use areviolated.

D. They do not require that samples be drawn from normal populations.

E. They can be used even if the population standard deviation is unknown.


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13. A Statistics teacher decides to giveA's only to students who score in the top15% on the final exam. The scores are normally distributed with a mean of 78and a standard deviation of 7 (this is also the population standard deviation).

To the nearest integer value, what is the lowest score a student could earn and

still receive anA?

A. 79

B. 80

C. 82

D. 83

E. 85

14. From the data in this table, what is P(B| E)?

A B Total

C 23 32 55D 15 15 30E 12 23 35

Total 50 70 120

A. 12/35

B. 12/55

C. 23/70

D. 35/70

E. 23/35

15. Which of the following are true statements?

I. An observational study differs from an experiment in that only experimentshave distinct groups upon which measurements are made.

II. A sample survey is one type of experiment.

III. Experiments, but not observational studies, can point to cause-and-effect

relationships.

A. I only

B. II only

C. III only

D. II and III only

E. I, II, and III


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16. Consider the following set of sample data: 21, 24, 25, 32, 35, 31, 29, 28. Whichof the following will give a 95% confidence interval for the mean of thepopulation from which this sample was drawn?

A. 28.125 1.96 (4.61/ 8 )

B. 28.125 2.365(4.31/ 8 )

C. 28.125 2.306(4.61/ 8 )

D. 28.125 2.365(4.61/ 8 )

E. 28.125 2.306(4.31/ 8 )

17. Which of the following are necessary in order to use a normal approximationto the sampling distribution of a sample proportion?

I. The population from which the sample was drawn must be at least 10 times

larger than the sample.

II. The population from which the samples are drawn must be normal.

III. The sample must be a simple random sample from the population.

A. I only

B. II only

C. III only

D. I and III onlyE. II and III only

18. What are the mean and median of the data presented in the table below?

Value RelativeFrequency

CumulativeFrequency

15 .15 .1518 .10 .2519 .20 .4523 .25 .70

27 .30 1.00

A. 21.7, 23

B. 21.7, 19

C. 21.7, 20

D. 20.4, 23

E. 20.4, 19


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19. A population is strongly skewed to the left with a mean of 18 and a standarddeviation of 4. You draw samples of size 4 from this population and calculatethe mean of each sample. Which of the following shows the mean, standard

deviation, and shape of the sampling distribution of the sample mean?

A. 18; 4; skewed to the leftB. 18; 2; approximately normal according to the Central Limit Theorem

C. 18; 2; skewed to the right

D. 18; 2; skewed to the left

E. 18; 4; approximately normal according to the Central Limit Theorem.

20. What is the "five-number summary" of the data given in the table below?

Value Relative

Frequency

Cumulative

Frequency

15 .15 .1518 .10 .2519 .20 .4523 .25 .7027 .30 1.00

A.15-18-19-23-27

B.15-18-19-23-23

C.15-18-23-27-27

D.15-18-18-23-27

E. 15-19-23-23-27


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A

B

C

D

E

CD

E

.7

.3

.3

.4

.3

.1

.5

.4

21. Given the tree diagram shown here, what is P(A | E)?

A. 7/11

B. 3/4

C. 4/7

D. 3/10

E. .21

22. Researchers conduct a study to determine whether an online statistics course

is superior to an in-class course in terms of success on the AP Exam. Theycompare the scores of 150 students, 75 of whom took each type of course. The

online students did better, on average, so the researchers publish an article

recommending that students who want to do well on the AP Exam shouldconsider the online course rather than a course at their school. Which of the

following statements is true?

A. The results of this study are meaningless because this was an observational studyand not an experiment.

B. Self-selection is nota factor when comparing the performance of the two groups.

C. This is an example of theplacebo effect.

D. Though there is a relationship between the type of course and performance, thisstudy does not show that there is a cause-and-effect relationship.

E. There is too much sampling error in this type of study to be able to makeconclusions.


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23. The table below gives (in seconds) the time required for six right-handedpeople to complete a test of dexterity, first with their left hand, then with theirright. You want to perform a t test to see if there is a significant difference

between the times required for the left and right hands. The appropriate

number of degrees of freedom for this test is:

Left Hand Right Hand

Alice23 19

Bob 19 18Carrie 17 18Doug 26 20

Eleanor 20 19Frank 22 20

A. 6

B. 12

C. 11

D. 10

E. 5

24. Two variables are related so that the slope of their regression line is 6, and so

that 35.and2.4 == xy ss . What is r, the correlation coefficient for the two

variables?

A. 1/12

B. 72

C. .6

D. .5

E. .54


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25. All 32 seniors at a High School took both the AP Exam in Statistics and the APExam in Calculus. Their mean score on the Statistics exam was 2.57 with astandard deviation of .7. Their mean score on the Calculus exam was 2.78 with

a standard deviation of .64. If we combine these tests into a single score, the

correct mean and standard deviation are:

A. 5.35; .7 +.64

B. 5.35, 64.7. +

C. 5.35, 22 64.7. +

D. 5.35, 22 64.7. +

E. The mean is 5.35, but you cannot determine the standard deviation from thisinformation.

26. You want to research a new pill you hope will relieve the effects of arthritis inpersons over 50 years of age. You divide your volunteers into two groups: oneconsisting of people aged 50-60 and one consisting of people over 60. You

further divide each of those groups by gender. The members of each of thesefour groups are randomly assigned to treatment and control groups with the

treatment group receiving the new pill and the control group receiving the

placebo. The basic design of this study is:

A. double-blind, blocked by age and gender.

B. comparative randomized, blocked by age, gender, and type of medication.

C. randomized and stratified.

D. completely randomized.E. comparative randomized, blocked by age and gender.

27. The final exam scores in freshman English at a large high school are normally

distributed with a mean of 84% and a standard deviation of 14. If 450 students

took the exam, approximately how many students scored between 70% and80%?

A. 103

B. 125

C. .2289

D. 99

E. 95


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28. You want to construct a 95% confidence interval for the proportion of patientswho will experience adverse reactions to a new medication. Because sideeffects can be rather severe, you desire a margin of error of no more than .05.

You have no idea, prior to doing the research, of what the true proportion

might be. What is the minimum number of subjects you will need in yourstudy?

A. 384

B. 385

C. 19.6

D. 1537

E. 390

29. A binomial event is observed 50 times. The probability of the event being

successful is .3. LetXequal the count of successes of the event during the 50trials. What are X and X ?

A. 15; 3.24

B. .3; .15

C. 15; 10.5

D. .15; 3.24

E. 15; 3.87


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30. You want to obtain a simple random sample of size 30 of all students in thejunior class. Assume there are 150 boys and 150 girls in the class. Which of thefollowing methods will produce such a sample?

I. Number the students from 1 to 300. Randomly select one of the first 10students, then take every tenth student on the list after that.

II. Number the students from 1 to 300. Use a random number generator toselect 30 numbers from 1 to 300. Your sample consists of the studentswhose names correspond to the generated numbers.

III. Number the boys from 1 to 150 and number the girls from 151 to 300.Randomly select 15 boys by using a random number generator to pick 15

numbers from 1 to 150. Then select 15 girls by using a random numbergenerator to pick 15 numbers from 151 to 300.

A. I only

B. II onlyC. III only

D. II and III only

E. I, II, and III

31. A study found that the hours students spend watching television and their

grade point averages (GPAs) have a correlation of r= .71. Given this

information, which of the following statements is most accurate?

A. About 71% of students' GPAs depend on hours spent watching television.

B. About half of the variation in GPAs can be explained by hours spent watchingtelevision.

C. A student could improve his/her GPA by watching less television.

D. There is a cause-and-effect relationship between watching television and success inschool.

E. For each decrease in one hour of television watching, there will be a correspondingincrease of .7 in a student's GPA.


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32. You conduct a2

test for independence to see if political affiliation is related

to gender in a medium-sized Midwestern town. The test is based on data from a

survey asking respondents to indicate their preference for one of four political

parties. Your2X value is 5.21. What P-value is associated with this value?

A. .05 .25

C. .15


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35. It is appropriate to use a matched pairs experimental design when:

A. both treatment and control groups are similar.

B. each subject is to receive both treatments.

C. you need a special technique for establishing a control group.D. a comparative randomized design is not feasible.

E. you need a control for confounding variables.


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36. Use this computer output to determine r, the correlation coefficient betweenMethod 1 and Method 2.

Descriptive Statistics

Variable N Mean Median TrMean StDev SEMeanMETHOD 1 12 64.42 66.50 64.70 7.10 2.05METHOD 2 12 63.25 63.50 63.30 7.28 2.10

Variable Min Max Q1 Q3METHOD 1 52.00 74.00 57.25 70.25METHOD 2 53.00 73.00 55.75 69.75

Regression Analysis

The regression equation is

Predictor Coef Stdev t-ratio pConstant 40.98 18.17 2.25 0.048METHOD 2 0.3705 0.2856 1.30 0.224

s = 6.892 R-sq = R-sq(adj) = 5.8%

A. .241

B. .380

C. .058D. .145

E. .027


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37. Which of the following gives a 99% confidence interval for the slope of theregression line from this computer output?

Descriptive Statistics

Variable N Mean Median TrMean StDev SEMeanMETHOD 1 12 64.42 66.50 64.70 7.10 2.05METHOD 2 12 63.25 63.50 63.30 7.28 2.10

Variable Min Max Q1 Q3METHOD 1 52.00 74.00 57.25 70.25METHOD 2 53.00 73.00 55.75 69.75

Regression Analysis

The regression equation is

Predictor Coef Stdev t-ratio pConstant 40.98 18.17 2.25 0.048METHOD 2 0.3705 0.2856 1.30 0.224

s = 6.892 R-sq = R-sq(adj) = 5.8%

A. 40.98 3.169(.286)

B. .371 3.055(.286)

C. .371 3.169(6.892)

D. .371 3.055(40.98)

E. .371 3.169(.286)


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38. Look at the scatterplot pictured here. Regarding the point markedA, which ofthese are true?I. Ais better described as an influential point rather than an outlier.

II. RemovingAfrom the scatterplot would cause the correlation to increase.

III. RemovingAfrom the scatterplot would cause the slope of the regressionline to decrease significantly.

A. I only

B. I and II only

C. II only

D. II and III only

E. III only

39. The IQs of students at a very prestigious technical university are normally

distributed with a mean of 124 and a standard deviation of 8. What is theprobability that a person selected at random from this population will have anIQ below 100?

A. .023

B. .0013

C. .005

D. .9987

E. 0


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40. A survey of 40 people finds that 22 prefer Sugar Crunchies breakfast cereal toHoney Yummies. Another completely independent survey finds that 24 of 50people surveyed prefer Sugar Crunchies to Honey Yummies. For a significancetest of the hypothesis 210 : ppH = , where 1p is the proportion favoring Sugar

Crunchies from the first survey population, and 2p is the proportion from the

second survey population, what is the standard error of the difference betweenthe proportions?

A.

+

50

1

40

1

50

24

40

22

B.50

50

231

50

23

40

40

221

40

22

+

C.

+

50

1

40

1

90

44

90

46

D.

+

50

1

40

1

90

24

90

22

E.90

50

231

50

23

90

40

221

40

22

+


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Free-Response Section (90 minutes)

After you finish answering these questions, correct your own work using the answer keyprovided, then send your corrected work back to your instructor. You'll be scored onwhether you did the work, not on how many questions you answered correctly.

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 you can in no more than 90minutes.

It's important to stay within the time limit to see how you'd do under real test conditions.Read over all the questions first, and do the questions you feel most confident about. Thengo back and do the questions you're less confident about. Stop at 90 minutes, and then usethe answer key to correct your work.

If you can't finish all the questions in 90 minutes, go back later and do the problems youweren't able to finish.

1. You draw samples of size nfrom the population of all pennies in circulation. The randomvariable of interest is the mean age of the pennies in the sample (current year penniesare considered to be zero years old). The distribution of ages of pennies (starting at 0) isknown to be skewed markedly to the right. That is, there are more recently mintedpennies than older pennies in the population. One scholar claims that the mean age ofall pennies in circulation is 7.4 years with a standard deviation of 3.3 years. Assume thatthis scholar is correct. Discuss the mean, standard deviation, and shape of the samplingdistribution of sample means of the ages of pennies for each of the given sample sizes.Where possible, give precise values.

A. n= 5

B. n= 15

C. n= 40

2. A sports car manufacturer paints its cars silver, white, black, and red in the followingproportions:

Color: Silver White Black Red

Proportion: .2 .3 .1 .4

We know that 40% of these cars are manufactured with tan leather upholstery while theremaining 60% are manufactured with gray leather.

A. Assuming that the choice of exterior color and leather color are independent,

what is the probability that a randomly selected sports car from thismanufacturer will be white with gray upholstery?

B. Assuming that we know the car has tan upholstery, what is the probability thatthe car is either silver or white?


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3. You are interested in conducting a survey at your school to determine if gender orethnicity is related to perceptions about educational opportunity. The school has 1,800students but you only have resources to interview 100. The student body isapproximately equally divided between males and females. Twelve percent of theschool's population is Asian American, 8% is African American, 10% is Native American,and 70% is Caucasian. You are interested in being able to generalize the results of yoursurvey to the entire student body.

A. Describe a technique for obtaining a sample of size 100 that would have areasonable chance of producing results that could be generalized to the entire

school.

B. Suppose you sent the surveys out to classes and asked the students to

complete them and return them to the main office. Would the returns be likely

to be biased in any direction? If so, why? In what direction?

C. Suppose you decide to conduct the survey by personal interview. Members of

the student council, all of whom happen to be Caucasian, will conduct personalinterviews with the selected students. One of the survey questions reads, "Doyou agree or disagree with the following statement: All students, regardless of

ethnicity, have equal opportunity to become part of student government."

What potential bias is present in this question?

4. The following table gives the inflation rate and the corresponding prime lending rate for7 different years. The equation of the regression line is:

primelendingrate = 3.175 + .654(inflationrate).

Inflation

Rate (x)

Prime Lending

Rate (y)

3.3 5.26.2 811 10.89.1 7.95.8 6.86.5 6.97.6 9

A. What is the predicted prime lending rate when the inflation rate stands at 6%?

B. What is the value of the residual when the inflation rate is 5.8%?

C. Interpret the slope of the regression line for this situation.

D. An eager economist uses these data to predict that the prime lending ratewould be 16.26 if the inflation rate rose to 20%. Comment on this prediction.


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5. The Director of Student Activities is concerned that she has not hired enough security forthe Sadie Hawkins Day dance, and wants to know approximately how many students willbe attending. If more than 25% of the student body is planning on going to the dance,she will need to hire more security. She sends out a survey to 300 students, and out ofthe 285 who respond, 82 say they plan to attend.

A. On the basis of this survey, should the Director of Student Activities hire more

security? Use appropriate statistical evidence to support your conclusion.

B. There were 15 people who didn't return their surveys. Suppose they had. Is it

possible that the Student Activities Director's decision would have been

different?

6. Suppose you have a friend on the school basketball team but, unfortunately, he is not agood free throw shooter. Over the course of his career, he has only made 40% of hisshots. Otherwise, he is a good player and gets fouled a lot so he shoots 10 free throws agame, on average. In the biggest game of the season, he does very well and makes 6

out of 10 free throw attempts.

A. Assuming that each shot is independent, set up the expression you would use

to determine the exactprobability that your friend actually makes 6 or more

free throws in a given game.

B. Using the set of random numbers shown here, explain how you would set up a

simulation to determine the probability of making 6 or more free throws out of10 attempts if your probability of making any one free throw is .4.

98713 19464 57512 49898 84837 52245 38816 62042 76406 8974451623 65847 53436 08320 45677 46304 71946 17871 88983 2594821826 94930 96270 97988 37221 07174 51855 00969 24384 9809541970 19537 18910 17433 36753 41545 01058 47896 75215 3599604853 00796 78602 54962 42771 39128 96541 47221 39264 05585

C. Suppose you wanted to do a normal approximation to the binomial for this

situation. What are the mean and standard deviation of the binomial

distribution? Is the normal approximation justified in this situation? Explainwhy or why not? Would the normal approximation be justified if n= 100?

D. One of your friend's attempts during a game is a "one-and-one." That is, if he

makes one free throw, he is given the opportunity to take a second shot.Assuming each shot is independent, is he most likely to make 0, 1, or 2 points

on a "one-and-one" opportunity.

E. What is the probability that the first free throw he makes is his fourth attempt?


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_____________ Copyright 2000 Apex Learning Inc All rights reserved This material is intended for the exclusive use of

TI-83 screens are used with the permission of the publisher. Copyright 1996, TexasInstruments, Incorporated.

MINITAB is a trademark of Minitab, Inc., and is used herein with the owner's permission.Portions of MINITAB Statistical Software input and output contained in this course areprinted with permission of Minitab, Inc.

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