Practice AP Statistics Exam

Saturday May 3, 2014

University of Delaware

Section I: Multiple Choice This exam is used by the kind permission of faculty at Clemson University, Clemson, SC.

Name: ____________________________________________________________

School: ___________________________________________________________

Instructions: 1. No electronic devices except an approved calculator are permitted, including cell phones and

dictionaries. If you brought a cell phone or an electronic device other than an approved calculator, please turn it off and put it away.

2. Calculators may not be shared. 3. Complete the Last Name and First Name sections on the scansheet. 4. Code your 3-digit Student ID Number in the Student ID Number space on your scansheet

and fill in the bubbles. Use the first 3 spaces only.

5. Code your 6-digit AP School Code in the Student ID Number space. Use the last 6 spaces.

School Name AP School Code Middletown HS 080092 Charter School of Wilmington 080164 Conrad Schools of Science 080228 Concord High School 080156 Unionville High School 394955 Brandywine High School 080158 AI Dupont High School 080155 Salesianum School 080195

6. Choose the best answer to each multiple choice question. DO NOT TURN THIS PAGE OVER UNTIL INSTRUCTED TO DO SO.

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STATISTICS

SECTION I

Time --- 1 hour and 30 minutes

Number of questions --- 40

Percent of total grade --- 50

1. The bar chart below shows the number of applicants to a graduate program that were admitted

and denied by gender.

Which of the following is true?

(A) More males than females were denied.

(B) Most applicants were female.

(C) A higher percentage of females were denied.

(D) More females than males were admitted.

(E) There were an equal number of male and female applicants.

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2. A fast food restaurant claims that the average time a customer waits in line at drive-thru windows at their stores is 1.8 minutes with a standard deviation of 0.45 minutes. A random sample of 34 customers’ times at the drive-thru at one particular location yielded a sample mean of 2.2 minutes. Assuming that the conditions for inference are met, which of the following is the correct interpretation for the p-value obtained from testing that the average amount of time spent in the drive-thru at this location is greater than the overall average given by the company?

(A) The p-value is the probability of obtaining a sample mean of 2.2.

(B) The p-value is the probability that these 34 customers waited longer than 1.8 minutes.

(C) The p-value is the probability of rejecting the null hypothesis if it is actually true.

(D) The p-value is the probability of obtaining a sample mean time of 2.2 minutes or greater if the actual average time is 1.8 minutes.

(E) The p-value cannot be interpreted with the information given.

3.

A manufacturer claims that the percentage of red gummy bears in each package of gummy bears is 17%. An AP Statistics class collected 10 randomly selected bags of 150 gummy bears each from this manufacturer. The class would like to determine if the proportion of red gummy bears from this manufacturer is greater than the company claims. Which of the following is a correct statement regarding performing a hypothesis test for this question, at the 0.05 level of significance?

(A) Need to assume the population from which this sample was drawn is normally distributed.

(B) If the test statistic is less than 0.05 the sample indicates that the proportion of red gummy bears from this manufacturer is different from 17%.

(C) For this test to result in a positive test statistic, the sample proportion would have to be greater than 17%.

(D) If the p-value is greater than 0.05 then we can conclude that the true proportion of red gummy bears is equal to 17%.

(E) Having any sample proportion greater than 17% indicates that the true proportion of red gummy bears is greater than 17%.

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4. A basketball coach wanted to know if the attendance at home games is related to the number of points his team scores. A simple linear regression analysis was performed and the partial computer output is given below.

Which of the following is true?

(A) Since the p-value for the slope is greater than .05 there is a strong correlation between attendance at home games and points scored.

(B) The critical value for a 95% confidence interval for the slope of the least squares regression line is t = — 0.618.

(C) The correlation coefficient for attendance at home games and points scored is approximately — 0.16.

(D) Approximately 4% of the variation in points scored can be explained by using attendance at home games to predict number of points scored.

(E) The slope indicates that as the number of people at the home games increases so do the number of points scored.

Dependent variable is: points scored R squared = 2.5% R squared (adjusted) = -4.0% s = 12.09 with 17 - 2 = 15 degrees of freedom Source Sum of Squares df Mean Square F-ratio Regression 55.7995 1 55.7995 0.382 Residual 2193.26 15 146.217 Variable Coefficient s.e. of Coeff t-ratio prob Constant 72.7212 11.64 6.25 < 0.0001 attendance -956.355e-6 0.001548 -0.618 0.5460

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5. A company providing cable television services wishes to determine the proportion of their customers that are satisfied with the quality of the services they receive. As the majority of their customers pay their bills on-line, the company has determined the most cost effective method for conducting a survey is to prompt a random sample of customers with on-line accounts to complete a customer satisfaction survey the next time they sign in to their account. Which of the following statements is true?

(A) The survey results will be biased if customers with on-line accounts differ from customers without on-line accounts with respect to their level of satisfaction.

(B) If enough customers complete the survey, then the survey results will not be biased.

(C) The survey results will be more meaningful if a control group is used.

(D) This survey method will result in a stratified sample of the company’s customers.

(E) This survey method will result in a simple random sample of the company’s customers.

6.

The length of NCAA college baseball games is normally distributed with a mean of 165 minutes and a standard deviation of 10 minutes. Let X represent the number of minutes in an NCAA college baseball game. Which of the following statements is equivalent to finding the probability that the amount of time an NCAA college baseball game lasts is less than 2 hours 30 minutes?

(A) 𝑃(𝑋 < 𝜇 + 1.5𝜎)

(B) 𝑃(𝑋 < 𝜇 + 2.5𝜎)

(C) 𝑃(𝑋 < 𝜇 − 2.5𝜎)

(D) 𝑃(𝑋 < 𝜇 − 1.5𝜎)

(E) 𝑃(𝑋 < 𝜎 + 1.5𝜇)

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7. The figure below illustrates two sampling distributions for sample proportions when the population proportion is p = 0.50.

Which of the following must be true about the sample sizes of these two sampling distributions?

(A) The sample size of I is greater than the sample size of II.

(B) The sample size of II is greater than the sample size of I.

(C) The sample sizes of I and II are equal.

(D) The sampling distribution of the sample proportion is not affected by sample size.

(E) There is not enough information provided to compare the sample sizes.

8.

Let X represent a random variable whose distribution is normal with a standard deviation of 5. What is the mean of X if P(X > 46) = 0.1151?

(A) —1.2

(B) 1.2

(C) 40.0

(D) 45.4

(E) 52.0

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9. Nearly 12,000 high school students across 11 different countries were surveyed about both their sleep habits and their performance in school. Based on the results, researchers concluded that a lack of sleep is linked to students earning poor grades in school. Which of the following statements is true?

(A) This is an observational study. Therefore, researchers cannot conclude that a lack of sleep causes poor grades.

(B) This is an observational study. Therefore, researchers can conclude that a lack of sleep causes poor grades.

(C) This study is a well-designed experiment. Therefore, researchers cannot conclude that a lack of sleep causes poor grades.

(D) This study is a well-designed experiment. Therefore, researchers can conclude that a lack of sleep causes poor grades.

(E) This is neither an observational study nor a well-designed experiment.

10.

A campaign researcher would like to estimate the proportion of registered voters that will vote for his candidate. He runs a poll each week asking registered voters their candidate preference and calculates a 95% confidence interval to estimate the true proportion of registered voters that will vote for his candidate. On week 39 his confidence interval was (0.52, 0.56). On week 40 (the last week of the campaign) he wants to conduct one final poll. He would like his 95% confidence interval to have a margin of error of .01. Use the previous week’s information to determine the minimum sample size needed to achieve the researcher’s goals for estimation.

(A) 96

(B) 9604

(C) 9543

(D) 11187

(E) 9589

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Questions 11-12 refer to the following scenario and graphical display.

The boxplots below illustrate the distribution of graduation rates for a sample of public universities and for a sample of private universities.

11. Based on the boxplots, which of the following statements is NOT true?

(A) The median graduation rate of the private schools is higher than the median graduation rate of the public schools.

(B) About 25% of the public schools have a graduation rate of 80% or higher.

(C) About 25% of the private schools have a graduation rate of 80% or higher. (D) The lowest observed graduation rate was for a public school.

(E) The highest observed graduation rate was for a private school.

12. Based on the boxplots, which of the following statements must be true?

(A) There is a little more variability in the graduation rates of the private schools than the public schools.

(B) The interquartile range of the private schools is equal to the interquartile range of the public schools.

(C) There are more data values for private schools than for public schools.

(D) There are more public schools with graduation rates less than 75% than there are private schools.

(E) There are more public schools with graduation rates less than 70% than there are private schools.

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13. The administration at a university is reconsidering its policy requiring all students to live on campus for their first year, and plans to survey a sample of the students about their opinion. As students with different class standings are likely to have differing views on the issue, the administration would like to obtain a sample that fairly represents the number of freshmen, sophomores, juniors, and seniors at the university. Which of the following would be the most appropriate sampling method to use?

(A) Convenience sampling

(B) Systematic sampling

(C) Simple random sampling

(D) Stratified random sampling

(E) Cluster sampling

14.

Data were collected on the survival times (in days) of 72 guinea pigs after they were injected with tubercle bacilli in a medical experiment. A histogram of the values is shown below.

Which of the following conclusions can be made from the graph?

(A) The mean survival time is greater than the median survival time.

(B) The mean survival time is less than the median survival time.

(C) The mean survival time is equal to the median survival time.

(D) The relationship between the mean and median cannot be determined without the survival time values.

(E) A larger sample size is needed to determine the relationship between the mean and median survival time.

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15. Suppose that 10% of all U.S. school-aged children suffer from Attention-Deficit Hyperactivity Disorder (ADHD). What is the probability that in a random sample of ten U.S. school-aged children, exactly one of them suffers from ADHD?

(A) 0

(B) 0.10

(C) 1

(D) (10 1)(0.9)1(0.1)9

(E) (10 1

)(0.1)1(0.9)9

16.

Of the registered voters in a particular district, 42% are Democrats, 38% are Republicans, and 20% are unaffiliated. The new healthcare reform bill is favored by only 19% of the Republican voters in this district. What percentage of voters in this district are Republicans that do NOT favor the healthcare reform bill?

(A) 19%

(B) 31%

(C) 38%

(D) 81%

(E) 93%

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17. A company that designs and manufactures women’s running shoes wants to determine whether or not they can claim that wearing their latest running shoe will result in faster 100-meter dash times than wearing their competitor’s most popular running shoe. Of the following, which is the best method for obtaining this information?

(A) Have the female subjects choose which of the two shoes they would like to wear, then compare their running times in a 100-meter dash.

(B) Assign the two shoes to the female subjects on the basis of their past 100-meter dash running times without randomization, then compare the results in a new race.

(C) Have all female subjects run the 100-meter dash twice, wearing a different pair of shoes each time. Require that everyone wear the company’s shoe in the first race. Compare the results.

(D) Have all female subjects run the 100-meter dash twice, wearing a different pair of shoes each time. Randomize whether they wear the company’s shoe in the first or second race. Compare the results.

(E) Have each female subject wear one of the company’s shoes and one of the competitor’s shoes in a 100-meter dash. Randomize whether the company’s shoe is worn on the left or right foot.

18.

Most of the houses in a large neighborhood have very similar prices. However, there are one or two very expensive houses, and one or two very inexpensive houses in this neighborhood. Which of the following best describes the relationship between the IQR and the standard deviation of the prices of the houses in this neighborhood?

(A) The IQR would be small and the standard deviation would be large.

(B) The IQR would be large and the standard deviation would be small.

(C) Both the IQR and the standard deviation would be large.

(D) Both the IQR and the standard deviation would be small.

(E) The IQR and the standard deviation will be equal in value.

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19. Bob and Joan were searching the Internet to find information on air travel in the United States. They found data on the number of commercial aircraft flying in the United States during the years 2000-2008. The dates were recorded as years since 2000 (thus, the year 2000 is recorded as year 0). They fit a least squares regression line to the data. The graph of the residuals and part of the computer output for the regression analysis are given below.

Predictor Coef Stdev t-ratio p Constant 2939.93 20.55 143.09 0.000 Years 233.517 4.316 54.11 0.000

What is the actual number of commercial aircraft flying in 2002 (rounded to the nearest whole number)?

(A) 2,472 flights

(B) 2,513 flights

(C) 3,022 flights

(D) 3,367 flights

(E) 3,447 flights

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20. A study was conducted to determine if the change in blood pressure after a month of exercise is larger for women than it is for men. Let µF represent the average change in blood pressure for females, µM represent the average change in blood pressure for males, and µD represent the average difference in blood pressure (blood pressure before exercise minus blood pressure after exercise) for all participants. Which of the following would be the null and alternative hypotheses for this study?

(A) H0: µF > µM and Ha: µF < µM

(B) H0: µD = 0 and Ha: µD > 0

(C) H0: µF < µM and Ha: µF > µM

(D) H0: µF = µM and Ha: µF > µM

(E) H0: µD > 0 and Ha: µD < 0

21.

To determine if there is a difference in males and females in their preference of the name brand salsa over the generic brand salsa, a random sample of 300 males and 450 females participated in a taste test. Of the men participating in the taste test, 192 preferred the name brand salsa. Of the females participating in the taste test, 324 preferred the name brand salsa. Which of the following statements is true?

(A) At the 5% significance level, there is sufficient evidence to suggest the proportion of males that prefer the name brand salsa is significantly higher than the proportion of females.

(B) At the 1% significance level, there is sufficient evidence to suggest the proportion of males that prefer the name brand salsa is significantly different than the proportion of females.

(C) At the 10% significance level, there is insufficient evidence to suggest there is significant difference between the proportion of males and females that prefer the name brand salsa.

(D) At the 5% significance level, there is sufficient evidence to suggest there is a significant difference between the proportion of males and females that prefer the name brand salsa.

(E) At the 1% significance level, there is sufficient evidence to suggest the proportion of males that prefer the name brand salsa is significantly higher than the proportion of females.

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Questions 22-23 refer to the following scenario.

On a roulette wheel there are 18 red slots, 18 black slots, and 2 green slots. Below are the counts for 1000 spins of the wheel. A chi-squared goodness of fit test is performed to see if this wheel is operating as a fair and level wheel.

Red Black Green

420 530 50

22.

What is the contribution to the chi-squared test statistic for the red slots?

(A) 473

(B) 12.8

(C) 6.86

(D) 6.08

(E) -6.08

23.

What are the appropriate degrees of freedom for this test?

(A) 999

(B) 998

(C) 3

(D) 2

(E) 1

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24. A local bakery sells its chocolate chip cookies in boxes of 12 (one dozen). The weights of each of the cookies are independent and are normally distributed with a mean of 22 grams and a standard deviation of 1 gram. The weights of the empty cookie boxes are normally distributed with a mean of 60 grams and a standard deviation of 2 grams. The weights of the boxes filled with one dozen cookies are expected to be normally distributed with a mean of 324 grams and a standard deviation of

(A) √3 grams

(B) √12 grams

(C) 4 grams

(D) √148 grams (E) 14 grams

25.

A 95% confidence interval was created to estimate the proportion of high school students that have smoked a cigarette. To create this interval, a random sample of 2000 high school students are selected. If we assume that everything else remains the same, what would happen to the margin of error if the sample size were increased to 6,000?

(A) The second margin of error would be the same as the original

(B) The second margin of error would be 6 times that of the original

(C) The second margin of error would be 3 times that of the original

(D) The second margin of error would be 16

the size of the original

(E) The second margin of error would be 13

the size of the original

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26. A meteorologist is interested in the relationship between the maximum wind speed and the central pressure of a hurricane. Based on a sample of 164 hurricanes, the least squares regression line is �̂� = 1133 – 1.07x, where x is central pressure (in millibars) and y is the maximum wind speed (in miles per hour). Which of the following best describes the slope of the least squares regression line?

(A) For each one millibar increase in pressure, the estimated maximum wind speed increases by 1.07 miles per hour.

(B) For each one millibar increase in pressure, the estimated maximum wind speed decreases by 1.07 miles per hour.

(C) For each one mile per hour increase in maximum wind speed, the estimated pressure increases by 1.07 millibars.

(D) For each one mile per hour increase in maximum wind speed, the estimated pressure decreases by 1.07 millibars.

(E) The slope has no meaning because the units of measure for x and y are not the same.

27.

Today’s weather report for your city states that the probability of rain is 0.60. Which of the following is the most reasonable explanation for how this probability could have been estimated?

(A) It has not rained in your city for the last two days, which increases the chance of rain for today to be above 0.50.

(B) It has rained in your city for the last two days, therefore it is likely, but not too likely, to rain again today.

(C) From the fact that, in a large number of days with atmospheric conditions similar to today, it rained in your city on 60% of those days.

(D) From the fact that it rained in your city on 60% of the days in this last year.

(E) From the fact that it is currently raining at 60% of the weather stations in the U. S.

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28. In a certain game of chance, a player is equally likely to earn 0, 1, or 2 points. The number of points earned in one game is independent of the number of points earned in a second game. Let �̅� represent the average number of points a player can earn when the game is played twice. Which of the following describes the sampling distribution of �̅�?

(A) �̅� 0 0.5 1 1.5 2

Probability 15 1

5

15

15

15

(B) �̅� 0 0.5 1 1.5 2

Probability 1

9 2

9

13

29

19

(C) �̅� 0 0.5 1 1.5 2

Probability 13 0 1

3 0 1

3

(D) �̅� 0 0.5 1 1.5 2

Probability 16 1

6

13

16

16

(E) It cannot be determined from the information given.

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29. A quality control engineer at the Hershey’s plant in Pennsylvania wants to test whether the production line machines are working properly. KIT KAT bars are advertised as weighing 1.5 ounces. The engineer will assume that the machines are working properly unless a test, based on a sample, supports shutting down the machines for repairs. Which of the following represents a consequence if the test resulted in a Type I error?

(A) The manufacturer does not shut down production to repair the machines and continues to produce bars that are significantly too small.

(B) A Type I error is not possible for this test.

(C) Another sample will need to be taken in order to make a decision about the repairs of the machines.

(D) The engineer obtains a sample mean that is not 1.5 ounces.

(E) The manufacturer spends money and hours repairing an unbroken machine.

30.

Control groups are used in experiments in order to

(A) control the placebo effect.

(B) group the subjects according to characteristics which are known to influence the response variable so as to control their effects.

(C) control nonresponse bias.

(D) eliminate voluntary response bias.

(E) double-blind the experiment.

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31. A 99% confidence interval is created to determine the population mean weight of college textbooks. The resulting interval is (2.45 lbs., 6.56 lbs.) based on a sample of 120 textbooks. Which of the following is the value of the margin of error for this interval?

(A) 4.11

(B) 4.505

(C) 2.055

(D) 0.798

(E) 2.575

32.

The national weather service tracks the number of days with snowfall in the state of Illinois for each month of the year. A researcher wants to know if Illinois had significantly more days with snowfall per month in 2013 than in 2000. A subset of the data collected is shown below. What is the most appropriate method for addressing the research question of interest?

Month 2000 2013

January 7 10

February 12 16

March 14 9

…. … …

December 18 19

(A) One proportion z-test

(B) One sample t-test for a mean

(C) Two proportion z-test

(D) Two sample t-test for means with independent samples

(E) Two sample t-test for means with dependent samples

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33. For two events A and B, P(A) = 0.40, P(B) = 0.30, and P(A or B) = 0.58. Which of the following statements must be true?

(A) A and B are independent, but not mutually exclusive.

(B) A and B are mutually exclusive, but not independent.

(C) A and B are both mutually exclusive and independent.

(D) A and B are neither mutually exclusive nor independent.

(E) There is not enough information provided to determine whether A and B are mutually exclusive or independent.

34.

The Centers for Disease Control (CDC) estimates that the proportion of US citizens that contracted the flu in 2013 was 12%. A town in Michigan (population 14,000) believes they have more cases of the flu than the national percentage. A random sample of 85 townspeople was selected, and it was found that 15 of them had contracted the flu in 2013. When performing a hypothesis test to determine if this town has a larger proportion of flu cases than the national percentage, to which of the following populations can the results of this test be safely generalized?

(A) 12% of US citizens in the year 2013

(B) All 14,000 townspeople in this town in 2013

(C) The 85 townspeople randomly selected in 2013

(D) All US citizens in the year 2013

(E) 17.6% of Michigan townspeople in the year 2013

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Questions 35-36 refer to the following scenario and set of data.

The two-way table below classifies each of 275 hurricanes by its month of occurrence and the maximum category reached.

Category 1 Category 2 Category 3 Category 4 Category 5 Total

June 11 6 1 1 0 19

July 14 6 3 0 0 23

Aug 29 18 22 5 2 76

Sept 37 22 34 9 1 103

Oct 16 18 12 3 0 49

Nov 3 2 0 0 0 5

Total 110 72 72 18 3 275

35. What percentage of category five hurricanes occurred in September?

(A) 0%

(B) 33.3%

(C) 66.7%

(D) 1%

(E) 3.6%

36.

Approximately what percentage of September hurricanes reached category five?

(A) 10%

(B) 33.3%

(C) 1%

(D) 66.7%

(E) 37%

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37. The scatterplot below shows the maximum wind speed (in miles per hour) versus the central pressure (in millibars) for 164 hurricanes.

Which of the following best describes the relationship between the two variables?

(A) The variables have a positive association because as central pressure increases, maximum wind speed tends to increase.

(B) The variables have a positive association because as central pressure increases, maximum wind speed tends to decrease.

(C) The variables have a negative association because as central pressure increases, maximum wind speed tends to decrease.

(D) The variables have a negative association because as central pressure increases, maximum wind tends to increase.

(E) The two variables have no association.

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38. The mean credit card debt for a U.S. household is $7,115 with a standard deviation of $2,160. This mean is such a large value because of a few deeply indebted households. If a random sample of 50 U.S. households is selected, what is the approximate probability that the mean credit card debt for the sample exceeds $7,500?

(A) 0.1038

(B) 0.4286

(C) 0.5714

(D) 0.8240

(E) The probability cannot be calculated because the population distribution is not normal.

39.

An insurance company selected a random sample of 250 of its life insurance claims in the year 1960. Of these 250 policyholders, 57 of them lived to be 100 years old. In a random sample of 500 life insurance claims from the year 2013, the insurance company determined that 133 of these policyholders lived to be 100 years old. What is the point estimate for a 95% confidence interval for the difference in the proportion of policyholders that lived to be 100 years old in 1960 and 2013?

(A) 54

(B) 1.96

(C) 0.437

(D) -0.038

(E) A point estimate is not appropriate because there are not equivalent sample sizes for the two populations.

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40. If the mean of a data set is 12.3 and the standard deviation is 0, then

(A) all of the observations are equal to 12.3.

(B) there must have been a mistake in the calculation, as it is not possible to have a standard deviation of 0.

(C) a histogram of the data set has a single peak at zero.

(D) a histogram of the data set will be strongly skewed.

(E) there is a large amount of variability in the data set.

END OF EXAMINATION