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

Percentage of total grade: 50

**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.

- Given the two boxplots above, which of the following statements is (are) true?
- The boxplot for Set B has more terms above its median than the boxplot for Set B.
- The boxplot for Set B has a larger IQR than the boxplot for Set A.
- The median for Set A is larger than the median for Set B.

- I only
- II only
- III only
- I and II only
- II and III only

- An advertiser is trying to decide which television station in town to use for his product. He gathers the ratings of all prime time shows on each network and constructs a boxplot of each. There are the same number of ratings for each network. The results are as follows:
- The median rating for Network A is greater than for Network B.
- The range for Network A is greater than for Network B.
- The interquartile ranges for the two networks are the same.
- The median rating for Network B is higher than for Network A.
- There are more ratings greater than 28 for Network A than for Network B.
- A statistics class wanted to construct a 90% confidence interval for the difference in the number of advanced degrees held by male and female faculty members at their school. They collected degree data from all the male and female faculty members and then used these data to construct the desired 90% confidence interval. Is this an appropriate way to construct a confidence interval?
- No, because we don't know that the distributions involved are approximately normal.
- Yes, but only if the number of men and the number of women are equal because our calculations will be based on difference scores.
- Yes, but only if the distribution of difference scores has no outliers or extreme skewness.
- No, because all the data were available, there is no need to construct a confidence interval for the true difference between the number of degrees.
- No, confidence intervals can only be constructed on independent samples, not on paired differences.

- You are interested in determining which of two brands of tires (call them Brand G and Brand F) last longer under differing conditions of use. Fifty Toyota Camrys are fitted with Brand G tires and 50 Honda Accords are fitted with Brand F tires. Each tire is driven 20,000 miles, and tread wear is measured for each tire, and the average tread wear for the two brands is compared. What is wrong with this experimental design?
- The type of car is a confounding variable.
- Average tread wear is not a proper measure for comparison.
- The experiment should have been conducted on more than two brands of cars.
- Not enough of each type of tire was used in the study.
- Nothing is wrong with this design—it should work quite well to compare the two brands of tires.

- The blood types of 468 people residing in the United States (all of whom were Asian, African-American, Arab, or White) were collected in a study to see if their blood type distribution is related to race. The following results were obtained:
- Yes, because the
*P*-value of the test is greater than 0.05. - Yes, because the
*P*-value of the test is less than 0.05. - No, because the
*P*-value of the test is greater than 0.05. - No, because the
*P*-value of the test is less than 0.05. *Χ*^{2}should not be used in this situation since more than 20% of the expected values are less than 5.- Most college-bound students take either the SAT (Scholastic Assessment Test) or the ACT (which originally stood for American College Testing). Scores on both the ACT and the SAT are approximately normally distributed. ACT scores have a mean of about 21 with a standard deviation of about 5. SAT scores have a mean of about 508 with a standard deviation of about 110. Nicole takes the ACT and gets a score of 24. Luis takes the SAT. What score would Luis have to have on the SAT to have the same standardized score (z-score) as Nicole's standardized score on the ACT?
- 548
- 574
- 560
- 583
- 588

- A researcher conducts a study of the effectiveness of a relaxation technique designed to improve the length of time a SCUBA diver can stay at a depth of 60 feet with a 80 cu. ft. tank of compressed air. The average bottom time for a group of divers before implementation of the program was 48 minutes and the average bottom time after implementation of the program was 54 minutes with a
*P*-value of 0.024. Which of the following is the best interpretation of this finding?- There is a 2.4% chance that the new technique is effective at increasing bottom time.
- If the new technique was not effective, there is only a 2.4% chance of getting 54 minutes or more by chance alone.
- 97.6% of the divers in the study increased their bottom times.
- We can be 97.6% confident that the new technique is effective at increasing bottom time.
- The new technique does not appear to be effective at increasing bottom time.

- Does ultraviolet radiation affect the birth rate of frogs? A study in the
*Tampa Tribune*reported that while 34 of 70 sun-shaded (from ultraviolet radiation) eggs hatched, only 31 of 80 unshaded eggs hatched. Which of the following would give a 99% confidence interval for the true difference between the proportions of shaded and unshaded eggs that hatched? - At Midtown University, the average weight of freshmen boys is 170 lbs with a standard deviation of 9 lbs The average weight of freshmen girls is 115 lbs with a standard deviation of 6 lbs. A new distribution is to be formed of the values obtained when the weights of the girls and the boys are added together. What are the mean and standard deviation of this new distribution? Assume that the weights of freshman boys and freshman girls are independent.
- 285, 15
- 285,117
- 55, 10.8
- 285, 10.8
- The mean is 285 but, under the conditions stated in the problem, you cannot determine the standard deviation.

- A random sample of 875 deaths in the United States in the year 2000 showed a mean life span of 75.1 years with a sample standard deviation of 16 years. These data were used to generate a 95% confidence interval for the true mean lifespan in the United States. The interval constructed was (74.0, 76.2). Which of the following statements is correct?
- There is a 95% chance that the average lifespan in the United States is between 74 and 76.2 years.
- 95% percent of the time, a person in the United States will live between 74 years and 76.2 years.
- 95% of the time, on average, intervals produced in this manner will contain the true mean lifespan.
- On average, 95% of people live less than 76.2 years.
- The probability is 0.95 that this interval contains the true mean lifespan in the United States.

- 10
- 30
- 5
- 9
- 15
- The following histograms compare two datasets (A and B):
- Sample A has more values than Sample B.
- The mean of Sample A is greater than the mean of Sample B.
- The mean of Sample B is greater than the mean of Sample A.
- The median of Sample A is greater than the median of Sample B.
- Both graphs are symmetric about their mean.
- Sometimes, the order in which a question is asked makes a difference in how it is answered. For example, if you ask people if they prefer chocolate or strawberry ice cream, you might get different answers than if you asked them if they prefer strawberry or chocolate ice cream. Seventy-five randomly selected people were asked, "Do you prefer chocolate or strawberry?" and 75 different randomly selected people were asked, "Do you prefer strawberry or chocolate?" The results are given in the following table.
- 0.453
- 0.096
- 0.56
- 0.055
- 0.19
- Young Atheart is interested in the extent to which teenagers might favor a dress code for high school students. He has access to a list of 55,000 teens in a large urban district. He draws a random sample of 40 students from this list and records the count of those who say they favor a dress code. He then repeats this process 24 more times. What kind of distribution has he simulated?
- The sampling distribution of a sample proportion with
*n*= 25 - The sampling distribution of a sample mean with
*n*= 40 - The binomial distribution with
*n*= 25 - The sampling distribution of a sample proportion with
*n*= 40 - The geometric distribution

- The sampling distribution of a sample proportion with
- Each of the histograms below is of 15 integers from 1 through 5. The horizontal and vertical scales are the same for each graph. Which graph has the
*smallest*standard deviation? - Which of the five histograms pictured below has the
*smallest*standard deviation? - Alligators captured in Florida are found to have a mean length of 2 meters and a standard deviation of 0.35 meters. The lengths of alligators are believed to be approximately normally distributed. What is the approximate length of an alligator at the 67th percentile of alligator lengths?
- 2.01 meters.
- 2.44 meters.
- 2.21 meters.
- 2.15 meters.
- 2.09 meters.

- Which of the following is not a property of the correlation coefficient
*r*is not a function of the units used for the variables.*r*can be calculated from either categorical or numerical variables.*r*is not affected by which variable is called*x*and which variable is called*y*.- |
*r*| ≥ 1. *r*is positive when the slope of the regression line is positive and negative when the slope of the regression line is negative.

- A study published in the
*Journal of the National Cancer Institute*(Feb. 16, 2000) looked at the association between cigar smoking and death from cancer. The data reported were as follows: - A former smoker is more likely to have died from cancer than a person who has never smoked.
- Former smokers and current smokers are equally likely to have died from cancer.
- The events "Current Smoker Dies from Cancer" and "Died from Cancer" are independent.
- It is more likely that a person who is a current smoker dies from cancer than a person has never smoked and dies from cancer.
- Among those whose death was not from cancer, the proportion of current smokers is higher than the proportion of former smokers.
- Which of the following is a reason for choosing a z-procedure rather than a t-procedure when making an inference about the mean of a population?
- The standard deviation of the population is unknown.
- The sample was a simple random sample.
- The sample size is greater than 40.
- The shape of the population from which the sample is drawn is approximately normal.
- The population standard deviation is known.

- You play a game that involves rolling a die. You either win or lose $1 depending on what number comes up on the die. If the number is even, you lose $1, and if it is odd, you win $1. However, the die is weighted and has the following probability distribution for the various faces:
- 0.50
- 0.10
- 0.45
- 0.22
- 0.55
- A psychiatrist is studying the effects of regular exercise on stress reduction. She identifies 40 people who exercise regularly and 40 who do not. Each of the 80 people is given a questionnaire designed to determine stress levels. None of the 80 people who participated in the study knew that they were part of a study. Which of the following statements is true?
- This is an observational study.
- This is a randomized comparative experiment.
- This is a double-blind study.
- This is a matched-pairs design.
- This is an experiment in which exercise level is a blocking variable.

- It is the morning of the day that Willie and Baxter have planned their long-anticipated picnic. Willie reads, with some distress, that there is a 65% probability of rain in their area today.
- It rains 65% of the time on this date each year.
- Historically, in the United States, it has rained 65% of the time on days with similar meteorological conditions as today.
- Historically, it rains 65% of the days during this month.
- Historically, in this area, it has rained 65% of the time on days with similar meteorological conditions as today.
- This is the result of a simulation conducted by the weather bureaus.
- In order to meet air pollution standards, the mean emission level for engines of a certain type must be less than 20 parts per million (ppm) of carbon. A study is to be done to determine if the engines from a particular company meet the standard. Which of the following represents the correct null and alternative hypotheses for this study? Let μ = the mean parts/million of carbon emitted for these cars.
*H*_{0}: μ = 20;*H*_{A}: μ > 20*H*_{0}: μ ≥ 20;*H*_{A}: μ < 20*H*_{0}: μ > 20;*H*_{A}: μ < 20*H*_{0}: μ = 20;*H*_{A}: μ ≥ 20*H*_{0}: μ ≥ 20;*H*_{A}: μ > 20

- Given P(A) = 0.60, P(B) = 0.30, and P(A|B) = 0.50. Find P(A U B).
- 0.90
- 0.18
- 0.40
- 0.72
- 0.75

- Assuming that each shot is independent, how many points is Baxter
*most*likely to make in a one-and-one situation?- 2
- 1
- 0
- 0.96
- None of these is correct.

- Assuming that each shot is independent, how many points will Baxter make
*on average*in a one-and-one situation?- 2
- 0.96
- 0
- 1
- 0.36

- The point marked with the "X" is better described as an outlier than as an influential point.
- Removing the point "X" would cause the correlation to increase.
- Removing the point "X" would have a significant effect on the slope of the regression line.
- I and II only
- I only
- II only
- II and III only
- I, II, and III
- A two-proportion large-sample confidence interval is to be constructed. Which of the following is
*not*usually considered necessary to construct such an interval?- The two samples should be SRSs from their respective populations.
- The two samples are independent.
- The populations from which the samples are drawn should each be approximately normal.
- The critical value is always z rather than
*t*.

- Results of an experiment or survey are said to be
*biased*if- Subjects are not assigned randomly to treatment and control groups.
- Some outcomes are systematically favored over others.
- There was no control group.
- A double-blind procedure was not used.
- The sample size was too small to control for sampling variability.

- 3.0
- 0.25
- 2.5
- 3.1
- 2.8
- A fair die is to be rolled 8 times. What is the probability of getting at least one 4?
- Which of the following statements is not true about the power of a statistical test?
- You can increase the power of a test by increasing the significance level.
- When
*H*_{0}is false, power = 1 – α. - The power of a test equals the probability of rejecting the null hypothesis.
- You can increase the power of a test by increasing the sample size.
- The power of a test is a function of the true value of the parameter being tested.

- 40% of the staff in a local school district have a master's degree. One of the schools in the district has only 4 teachers out of 15 with a master's degree. You are asked to design a simulation to determine the probability of getting this few teachers with master's degrees in a group this size. Which of the following assignments of the digits 0 through 9 would be appropriate for modeling this situation?
- Assign "0,1,2" as having a master's degree and "4,5,6,7,8,9" as not having a degree.
- Assign "1,2,3,4,5" as having a master's degree and "0,6,7,8,9" as not having a degree.
- Assign "0,1" as having a master's degree and "2,3,4,5,6,7,8,9" as not having a degree.
- Assign "0,1,2,3" as having a master's degree and "4,5,6,7,8,9" as not having a degree.
- Assign "7,8,9" as having a master's degree and "0,1,2,3,4,5,6," as not having a degree.

- Which of the following statements is (are) true about the
*t*-distribution?- Its mean, median, and mode are all equal.
- The
*t*-distribution is more spread out than the*z*-distribution. - The greater the number of degrees of freedom, the greater the variance of a
*t*-distribution.

- I only
- II only
- III only
- I and II only
- I and III only

- A study showed that persons who ate two carrots a day have significantly better eyesight than those who eat fewer than one carrot a week. Which of the following statements is (are) correct?
- This study provides evidence that eating carrots contributes to better eyesight.
- The general health consciousness of people who eat carrots could be a confounding variable.
- This is an observational study and not an experiment.

- I only
- III only
- I and II only
- II and III only
- I, II, and III

- You are designing a study to determine which of three brands of golf ball will travel the greatest distance. You intend to use only adult male golfers. There is evidence to indicate that the temperature at the time of the test affects the distance traveled. There is no evidence that the size of the golfer is related to the distance traveled (distance seems to have more to do with technique than bulk). This experiment would best be done
- by blocking on type of golf ball.
- by blocking on size of the golfer.
- by blocking on size of the golfer and temperature.
- without blocking.
- by blocking on temperature.

- Given the cumulative frequency table shown below, what are the mean and median of the distribution?
- Mean = 5.6, median = 7
- Mean = 5.6, median = 5
- Mean = 5.4, median = 7
- Mean = 5.4, median = 5
- Mean = 4.8, median = 6

- A spelling test was given to 1000 elementary students in a large urban school district. The graph below is a cumulative frequency graph of the results. Which of the following is closest to the five-number summary (minimum, first quartile, median, third quartile, maximum) for the distribution of spelling scores?
- {10, 30, 50, 70, 90}
- {10, 20, 50, 80, 90}
- {0, 30, 50, 70, 100}
- {20, 40, 60, 80, 100}
- There is not enough information contained in the graph to determine the five-number summary.
- A well-conducted poll showed that 46% of a sample of 1500 potential voters intended to vote for Geoffrey Sleazy for governor. The poll had a reported margin of error of 3%. Which of the following best describes what is meant by "margin of error of 3%"?
- The probability is 0.97 that between 43% and 49% will vote for candidate Sleazy.
- Ninety-seven percent of the time, between 43% and 49% would vote for candidate Sleazy.
- Between 43% and 49% of voters will vote for Sleazy.
- Three percent of those interviewed refused to answer the question.
- The proportion of voters who will vote for Sleazy is likely to be between 43% and 49%.

Based on these boxplots, which of the following is a correct conclusion about the relative ratings for the two networks?

From these data, a *Χ*^{2} value of 19.59 (df = 9) was computed. At the 5% level of significance, do these data indicate that Ethnicity and Blood Type are related?

Which of the following is the best estimate of the standard deviation for the approximately normal distribution pictured?

Which of the following statements is true?

A two-proportion z-test was performed on these data to see if the order of the question made a difference. What is the *P*-value of the test (hint: you need to think about whether this is a one-sided or a two-sided test)?

Which of the following statements is true?

Given that you win rather than lose, what is the probability that you rolled a "5"?

Which of the following best describes the most likely way that probability was arrived at?

Use the following information to answer questions 26–27:

Baxter is a 60% free-throw shooter who gets fouled during a game and gets to shoot what is called a "one-and-one" (that is, he gets to take a second shot—a bonus—if and only if he makes his first shot; each free throw, if made, is worth one point). Baxter can make 0 points (because he misses his first shot), 1 point (he makes the first shot, but misses the bonus), or 2 points (he makes his first shot and the bonus).

For the graph given above, which of the following statements is (are) true?

Given the probability histogram pictured for a discrete random variable X, what is μ_{x} ?

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