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# AP Statistics Practice Exam 1

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Below is a practice exam for AP statistics.  There are two sections in this practice exam.  Section I has 40 multiple choice questions.  Section II has 6 free response questions.  For a thorough review of the concepts in this practice example, refer to the information center on AP Statistics Notes.

### SECTION I

Time: 1 hour and 30 minutes

Number of questions: 40

Directions: Solve each of the following problems. Decide which is the best of the choices given and answer in the appropriate place on the answer sheet. No credit will be given for anything written on the exam. Do not spend too much time on any one problem.

1. A poll was conducted in the San Francisco Bay Area after the San Francisco Giants lost the World Series to the Anaheim Angels about whether the team should get rid of a pitcher who lost two games during the series. Five hundred twenty-five adults were interviewed by telephone, and 55% of those responding indicated that the Giants should get rid of the pitcher. It was reported that the survey had a margin of error of 3.5%. Which of the following best describes what is meant by a 3.5% margin of error?
1. About 3.5% of the respondents were not Giants fans, and their opinions had to be discarded.
2. It's likely that the true percentage that favor getting rid of the pitcher is between 51.5% and 58.5%.
4. About 3.5% of those contacted said they had no opinion on the matter.
5. About 3.5% thought their answer was in error and are likely to change their mind.
2. A distribution of SAT Math scores for 130 students at a suburban high school provided the following statistics: Minimum: 485; First Quartile: 502; Median: 520; Third Quartile: 544; Maximum: 610; Mean: 535; Standard Deviation: 88. Define an outlier as any score that is at least 1.5 times the interquartile range above or below the quartiles. Which of the following statements is most likely true?
1. The distribution is skewed to the right and there are no outliers.
2. The distribution is skewed to the right and there is at least one outlier.
3. The distribution is skewed to the left and there is at least one outlier.
4. The distribution is skewed to the left and 65 students scored better than 520.
5. The distribution is skewed to the right and 65 students scored better than 535.
3. A 2008 ballot initiative in California sought a constitutional ban on same-sex marriage. Suppose a survey prior to the election asked the question, "Do you favor a law that would eliminate the right of same-sex couples to marry?" This question could produce biased results. Which of the following is the most likely reason?
1. The wording of the question could influence the response.
2. Same-sex couples are likely to be underrepresented in the sample.
3. Only those who feel strongly about the issue are likely to respond.
4. Not all registered voters who respond to the survey are likely to vote.
5. Married couples are likely to vote the same way.
4. Two plans are being considered for determining resistance to fading of a certain type of paint. Some 1500 of 9500 homes in a large city are known to have been painted with the paint in question. The plans are:
5. Plan A:

1. Random sample 100 homes from all the homes in the city.
2. Record the amount of fade over a 2-year period.
3. Generate a confidence interval for the average amount of fade for all 1500 homes with the paint in question.

Plan B:

1. Random sample 100 homes from the 1500 homes with the paint in question.
2. Record the amount of fade over a 2-year period.
3. Generate a confidence interval for the average amount of fade for all 1500 homes with the paint in question.
1. Choose Plan A over Plan B.
2. Either plan is good—the confidence intervals will be the same.
3. Neither plan is good—neither addresses the concerns of the study.
4. Choose Plan B over Plan A.
5. You can't make a choice—there isn't enough information given to evaluate the two plans.
6. Let X be a random variable that follows a t-distribution with a mean of 75 and a standard deviation of 8. Which of the following is (are) equivalent to P(X > 65)?
1. P(X < 85)
2. P(X ≥ 65)
3. 1 – P(X < 65)
1. I only
2. II only
3. III only
4. I and III only
5. I, II, and III
7. Which of the following is the best description of a systematic random sample?
1. A sample chosen in such a way that every possible sample of a given size has an equal chance to be the sample.
2. After a population is separated into distinct groups, one or more of these groups are randomly selected in their entirety to be the sample.
3. A value is randomly selected from an ordered list and then every nth value in the list after that first value is selected for the sample.
4. Select a sample in such a way that the proportion of some variables thought to impact the response is approximately the same in the sample as in the population.
5. A sample in which respondents volunteer their response.
8. In a famous study from the late 1920s, the Western Electric Company wanted to study the effect of lighting on productivity. They discovered that worker productivity increased with each change of lighting, whether the lighting was increased or decreased. The workers were aware that a study was in progress. What is the most likely cause of this phenomenon? (This effect is known as the Hawthorne Effect.)
1. Response bias
2. Absence of a control group
3. Lack of randomization
4. Sampling variability
5. Undercoverage
9. Chris is picked up by the police for stealing hubcaps, but claims that he is innocent, and it is a case of mistaken identity. He goes on trial, and the judge somberly informs the jury that Chris is innocent until proved guilty. That is, they should find him guilty only if there is overwhelming evidence to reject the assumption of innocence. What risk is involved in the jury making a Type-I error?
1. He is guilty, but the jury finds him innocent, and he goes free.
2. He is innocent, and they find him innocent, and he goes free.
3. He is innocent, but the jury finds him guilty, and he goes to jail.
4. He is guilty, and they find him guilty, and he goes to jail.
5. He is guilty, and they correctly reject the assumption of innocence.
10. Given P(A) = 0.4, P(B) = 0.3, P(B|A) = 0.2.
11. What are P(A and B) and P(A or B)?

1. P(A and B) = 0.12, P(A or B) = 0.58
2. P(A and B) = 0.08, P(A or B) = 0.62
3. P(A and B) = 0.12, P(A or B) = 0.62
4. P(A and B) = 0.08, P(A or B) = 0.58
5. P(A and B) = 0.08, P(A or B) = 0.70
12. A study is to be conducted on a new weatherproofing product for outdoor decks. Four houses with outdoor decks in one suburban neighborhood are selected for the study. Each deck is to be divided into two halves, one half receiving the new product and the other half receiving the product the company currently has on the market. Each of the four decks is divided into North/South sections. Either the new or the old product is randomly assigned to the North side of each of the decks and the other product is assigned to the South side. The major reason for doing this is that
1. the study is much too small to avoid using randomization.
2. there are only two treatments being studied.
3. this controls for known differences in the effect of the sun on the North and South sides of decks.
4. randomization is a necessary element of any experiment.
5. this controls for the unknown differential effects of the weather on the North and South sides of decks in this neighborhood.
13. Which of the following best describes a cluster sample of size 20 from a population of size 320?
1. All 320 names are written on slips of paper and the slips are put into a box. Twenty slips are selected at random from the box.
2. The 320 names are put into an alphabetical list. One of the first 16 names on the list is selected at random as part of the sample. Every 16th name on the list is then selected for the sample.
3. The sample will consist of the first 20 people who volunteer to be part of the sample.
4. Each of the 320 people is assigned a number. Twenty numbers are randomly selected by a computer and the people corresponding to these 20 numbers are the sample.
5. The 320 names are put into an alphabetical list and the list numbered from 1 to 320. A number between 1 and 304 (inclusive) is selected at random. The person corresponding to that number and the next 19 people on the list are selected for the sample.
14. You are going to conduct an experiment to determine which of four different brands of cat food promotes growth best in kittens ages 4 months to 1 year. You are concerned that the effect might vary by the breed of the cat, so you divide the cats into three different categories by breed. This gives you eight kittens in each category. You randomly assign two of the kittens in each category to one of the four foods. The design of this study is best described as:
1. randomized block, blocked by breed of cat and type of cat food.
2. randomized block, blocked by type of cat food.
3. matched pairs where each two cats are considered a pair.
4. a controlled design in which the various breed of cats are the controls.
5. randomized block, blocked by breed of cat.
15.
16. The boxplots above compare the television ratings for two competing networks. What conclusion(s) can you draw from the boxplots?

1. Network A has more shows than Network B.
2. Network A has a greater range of ratings than Network B.
3. Network A is higher rated than Network B.
1. I and II only
2. II and III only
3. I and III only
4. I, II, and III
5. III only
17. A hypothesis test was used to test H0 : μ = 0.3 vs. HA : μ ≠ 0.3. The finding was significant for α = 0.05 but not for α = 0.04. A two-sided confidence interval for μ is constructed. Which of the following is the smallest confidence level for which the confidence interval will not contain 0.3?
1. 90%
2. 92%
3. 95%
4. 99%
5. 96%
18. Two months before a statewide election, 532 respondents in a poll of 1000 randomly selected registered voters indicated that they favored Candidate A for governor . One month before the election, a second poll of 900 registered voters was conducted and 444 respondents indicated that they favored Candidate A . A 95% two-proportion z confidence interval for the true difference between the proportions favoring Candidate A in the first and second polls was constructed and found to be (– 0.0063, 0.0837). Which of the following is the best interpretation of this interval?
1. There has not been a significant drop in support for Candidate A.
2. There has been a significant drop in support for Candidate A.
3. There has been no change in support for Candidate A.
4. At the 5% level of significance, a test of H0 : p1 = p2 vs. HA : p1 > p2 would yield exactly the same conclusion as the found confidence interval.
5. Since support for Candidate A has fallen below 50%, she is unlikely to win a majority of votes in the general election.
19. A kennel club argues that 50% of dog owners in its area own Golden Retrievers, 40% own Shepherds of one kind or another, and 10% own a variety of other breeds. A random sample of 50 dogs from the area turns up the data in the following table:
20. What is the value of the X2 statistic for the goodness-of-fit test on these data?

1. 3.56
2. 2.12
3. 4.31
4. 3.02
5. 2.78
21. A poll is taken to measure the proportion of voters who plan to vote for an ex-actor for Governor. A 95% confidence interval is constructed, based on a sample survey of prospective voters. The conditions needed to construct such an interval are present and the interval constructed is (0.35, 0.42). Which of the following best describes how to interpret this interval?
1. The probability is 0.95 that about 40% of the voters will vote for the ex-actor.
2. The probability is 0.95 that between 35% and 42% of the population will vote for the ex-actor.
3. At least 35%, but not more than 42%, of the voters will vote for the ex-actor.
4. The sample result is likely to be in the interval (0.35, 0.42).
5. It is likely that the true proportion of voters who will vote for the ex-actor is between 35% and 42%.
22. Two sampling distributions of a sample mean for a random variable are to be constructed. The first (I) has sample size n1 = 8 and the second (II) has sample size n2 = 35 . Which of the following statements is not true?
1. Both sampling distributions I and II will have the same mean.
2. Distribution I is more variable than Distribution II.
3. The shape of Distribution I will be similar to the shape of the population from which it was drawn.
4. The shape of each sampling distribution will be approximately normal.
5. The shape of Distribution II will be approximately normal.
23. A researcher wants to determine if a newly developed anti-smoking program can be successful. At the beginning of the program, a sample of 1800 people who smoked at least 10 cigarettes a day were recruited for the study. These volunteers were randomly divided into two groups of 900 people. Each group received a set of anti-smoking materials and a lecture from a doctor and a cancer patient about the dangers of smoking. In addition, the treatment group received materials from the newly developed program. At the end of 2 months, 252 of the 900 people in the control group (the group that did not receive the new materials) reported that they no longer smoked. Out of the 900 people in the treatment group, 283 reported that they no longer smoked. Which of the following is an appropriate conclusion from this study?
1. Because the P-value of this test is greater than α = 0.05, we cannot conclude that the newly developed program is significantly different from the control program at reducing the rate of smoking.
2. Since the proportion of people who have quit smoking in the experimental group is greater than in the control group, we can conclude that the new program is effective at reducing the rate of smoking.
3. Because the P-value of this test is less than α = 0.05, we can conclude that the newly developed program is significantly different from the control program at reducing the rate of smoking.
4. Because the difference in the proportions of those who have quit smoking in the control group (28%) and the experimental group (31.4%) is so small, we cannot conclude that there is a statistically significant difference between the two groups in terms of their rates of quitting smoking.
5. The standard deviation of the difference between the two sample proportions is about 0.022. This is so small as to give us good evidence that the new program is more effective at reducing the rate of smoking.

Questions 20 and 21 refer to the following information:

At a local community college, 90% of students take English. 80% of those who don't take English take art courses, while only 50% of those who do take English take art.

1. What is the probability that a student takes art?
1. 0.80
2. 0.53
3. 0.50
4. 1.3
5. 0.45
2. What is the probability that a student who takes art doesn't take English?
1. 0.08
2. 0.10
3. 0.8
4. 0.85
5. 0.15
3. Which of the following is the best reason to use a t-distribution rather than a normal distribution when testing for a population mean?
1. You should always use a t-distribution for small samples.
2. You are unable to compute the sample standard deviation.
3. The normal distribution is too variable.
4. The population standard deviation is unknown.
5. t-distributions are very similar to the normal distribution for large samples.
4. A study of 15 people ages 5 through 77 was conducted to determine the amount of leisure time people of various ages have. The results are shown in the following computer printout:
5. Which of the following is the 99% confidence interval for the true slope of the regression line?

1. 0.00935 ± 3.012(0.07015)
2. 0.00935 ± 2.977(5.628)
3. 7.845 ± 3.012(0.07015)
4. 0.00935 ± 2.977(0.07015)
5. 0.00935 ± 3.012(5.628)
6. You want to conduct a survey to determine the types of exercise equipment most used by people at your health club. You plan to base your results on a random sample of 40 members. Which of the following methods will generate a random simple random sample of 40 of the members?
1. Mail out surveys to every member and use the first 40 that are returned as your sample.
2. Randomly pick a morning and survey the first 40 people who come in the door that day.
3. Divide the number of members by 40 to get a value k. Choose one of the first kth names on the list using a random number generator. Then choose every kth name on the list after that name.
4. Put each member's name on a slip of paper and randomly select 40 slips.
5. Get the sign-in lists for each day of the week, Monday through Friday. Randomly choose 8 names from each day for the survey.
7. The following numbers are given in ascending order: 3, 4, x, x, 9, w, 13, 28, y, z. Which of the following gives a five-number summary of the data?
1. {3, 4, 9, 13, 28]
2. {3, x, w, 28, z}
3. There isn't enough information to identify all five numbers in the five-number summary.
8. The salaries and years of experience for 50 social workers was collected and a regression analysis was conducted to investigate the nature of the relationship between the two variables. R-sq. = 0.79. The results are as follows:
9. Which of the following statements is least correct?

1. There is a statistically significant predictive linear relationship between Years of Experience and Salary.
2. The residual plot indicates that a line is a good model for the data for all years.
3. There appears to be an outlier in the data at about 28 years of experience.
4. The variability of salaries increases as years of experience increases.
5. For each additional year of experience, salary is predicted to increase by about \$2141.
10. A wine maker advertises that the mean alcohol content of the wine produced by his winery is 11%. A 95% confidence interval, based on a random sample of 100 bottles of wine yields a confidence interval for the true alcohol content of (10.5, 10.9) Could this interval be used as part of a hypothesis test of the null hypothesis H0: p = 0.11 versus the alternative hypothesis HA: p ≠ 0.11 at the 0.05 level or confidence?
1. No, you cannot use a confidence interval in a hypothesis test.
2. Yes, because 0.11 is not contained in the 95% confidence interval, a two-sided test at the 0.05 level of significance would provide good evidence that the true mean content is different from 11%.
3. No, because we do not know that the distribution is approximately normally distributed.
4. Yes, because 0.11 is not contained in the 95% confidence interval, a two-sided test at the 0.05 level of significance would fail to reject the null hypothesis.
5. No, confidence intervals can only be used in one-sided significance tests.
11. Tom's career batting average is 0.265 with a standard deviation of 0.035. Larry's career batting average is 0.283 with a standard deviation of 0.029. The distribution of both averages is approximately normal. They play for different teams and there is reason to believe that their career averages are independent of each other. For any given year, what is the probability that Tom will have a higher batting average than Larry?
1. 0.389
2. 0.345
3. 0.589
4. 0.655
5. You cannot answer this question since the distribution for the difference between their averages cannot be determined from the data given.
12. An advice columnist asks readers to write in about how happy they are in their marriages. The results indicate that 79% of those responding would not marry the same partner if they had it to do all over again. Which of the following statements is most correct?
1. It's likely that this result is an accurate reflection of the population.
2. It's likely that this result is higher than the true population proportion because persons unhappy in their marriages are most likely to respond.
3. It's likely that this result is lower than the true population proportion because persons unhappy in their marriages are unlikely to respond.
4. It's likely that the results are not accurate because people tend to lie in voluntary response surveys.
5. There is really no way of predicting whether the results are biased or not.
13. A national polling organization wishes to generate a 98% confidence interval for the proportion of voters who will vote for candidate lam Sleazy in the next election. The poll is to have a margin of error of no more than 3%. What is the minimum sample size needed for this interval?
1. 6032
2. 1508
3. 39
4. 6033
5. 1509
14. In a test of the hypothesis H0: p = 0.7 against HA: p > 0.7 the power of the test when p = 0.8 would be greatest for which of the following?
1. n = 30, α = 0.10
2. n = 30, α = 0.05
3. n = 25, α = 0.10
4. n = 25, α = 0.05
5. It cannot be determined from the information given.
15. A research team is interested in determining the extent to which food markets differ in prices for store-brand items and the same name brand items. They identify a "shopping basket" of 10 items for which they know store-brand and name-brand items exist (e.g, peanut butter, canned milk, grape juice, etc.). In order to control market-to-market variability, they decide to conduct the study only at one major market chain and will select just one market in each of twelve geographically diverse cities. For each market selected they will compute the mean for the 10 store-brand items (call it ) and also for the 10 name-brand items (). They then intend to conduct a two-sample t-test (H0 : μN – μS = 0 vs. HA : μN – μS > 0) in order to determine if there is a statistically significant difference between the average prices of the two types of items. This procedure is not appropriate because
1. the sample sizes are too small to use a twosample test.
2. the variances are most likely not the same.
3. there is no randomization of treatments.
4. the samples are not independent.
5. they should be using a two-sample z-test.
16. A researcher was interested in determining the relationship between pulse rate (in beats/minute) and the time (in minutes) it took to swim a fixed distance. Based on 25 trials in the pool, the correlation coefficient between time and pulse rate was found to be –0.654 (that is, large times—going slowly—were associated with slower pulses). Prior to publication, the researcher decided to change the time measurements to seconds (each of the 25 times was multiplied by 60). What would this conversion do to the correlation between the two variables?
1. Since the units on only one of the variables was changed, the correlation between the two variables would decrease.
2. The correlation would change proportional to the change in the units for time.
3. The correlation between the two variables would change, but there is no way, based on the information given, to know by how much.
4. Changing the units of measurement has no effect on the correlation coefficient. Hence, the correlation would be the same.
5. Since changing from minutes to seconds would result in larger times, the correlation would actually increase.
17. The following histogram displays the scores of 33 students on a 20-point Introduction to Statistics quiz. The lowest score, 0, is an outlier. The next lowest score, 2, is not an outlier.
18. Which of the following boxplots best represents the data shown in the histogram?

19. For which one of the following distributions is the mean most likely to be less than the median?
20. An SAT test preparation program advertises that its program will improve scores on the SAT test by at least 30 points. Twelve students who have not yet taken the SAT were selected for the study and were administered the test. The 12 students then went through the 3-week testprep course. The results of the testing were as follows:
21. Assuming that the conditions necessary to conduct the test are present, which of the following significance tests should be used to determine if the test-prep course is effective in raising score by the amount claimed?

1. A two-sample t-test
2. A chi-square test of independence
3. A one-sample t-test
4. A t-test for the slope of a regression line
5. A two-sample z-test
22. Which of the following statements is (are) correct?
1. The area under a probability density curve for a continuous random variable is 1.
2. A random variable is a numerical outcome of a random event.
3. The sum of the probabilities for a discrete random variable is 1.
1. II only
2. I and II
3. I and III
4. II and III
5. I, II, and III
23. Let X be the number of points awarded for winning a game that has the following probability distribution:
24. Let Y be the random variable whose sum is the number of points that results from two independent repetitions of the game. Which of the following is the probability distribution for Y ?

25. Each of the following histograms represents a simulation of a sampling distribution for an estimator of a population parameter. The true value of the parameter is X, as shown on the scale. The domain of possible outcomes is the same for each estimator and the frequency axes (not shown) are the same. Which histogram represents the best estimator of X?
26. A weight-loss clinic claims an average weight loss over 3 months of at least 15 pounds. A random sample of 50 of the clinic's patrons shows a mean weight loss of 14 pounds with a standard deviation of 2.8 pounds. Assuming the distribution of weight losses is approximately normally distributed, what is the most appropriate test for this situation, the value of the test statistic, and the associated P-value?
1. z-test; z = –2.53; P-value = 0.0057
2. t-test; t = –2.53; 0.01 < P-value < 0.02
3. z-test; z = 2.53; P-value = 0.0057
4. t-test; t = –2.53; 0.005 < P-value < 0.01
5. z-test; z = 2.53; P-value = 0.9943

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