AP Statistics - Final Exam Study Guide (V.2)
35. Scientists working for a water district measure the water level in a lake each day. The daily water level in the lake varies due to weather conditions and other factors. The daily water level has a distribution that is approximately normal with mean water level of 84.07 feet. The probability that the daily water level in the lake is at least 100 feet is 0.064. Which of the following is closest to the probability that on a randomly selected day the water level in the lake will be at least 90 feet? (A) 0.29 (B) 0.31 (C) 0.34 (D) 0.37 (E) 0.50
(A) 0.29
40. To investigate the relationship between age and preference for two mayoral candidates in an upcoming election, a random sample of city residents was surveyed. The residents were asked which candidate they preferred, and each resident was classified into one of three age-groups. The test statistic for the appropriate hypothesis test was 3.7408. Approximately what is the probability that the observed responses would be as far or farther from the expected responses if there is no association between age-group and preference? (A) 0.0001 (B) 0.1541 (C) 0.2908 (D) 0.5873 (E) 0.7117
(B) 0.1541
37. An international polling agency estimates that 36 percent of adults from Country X were first married between the ages of 18 and 32, and 26 percent of adults from Country Y were first married between the ages of 18 and 32. Based on the estimates, which of the following is closest to the probability that the difference in proportions between a random sample of 60 adults from Country X and a random sample of 50 adults from-Country Y (Country X minus Country Y) who were first married between the ages of 18 and 32 is greater than 0.15? (A) 0.1398 (B) 0.2843 (C) 0.4315 (D) 0.5685 (E) 0.7157
(B) 0.2843
38. A consumer group wanted to investigate the relationship between the number of items purchased at a single visit to the local grocery store and the total cost of the items purchased. The group obtained a random sample of 11 receipts from the store and recorded the total number of items and the total cost from each receipt. The computer output of an analysis of total cost versus number of items purchased is shown in the table. Assume all conditions for inference were met. Based on the results shown in the table, which of the following is a 95 percent confidence interval for the average change in total cost for each increase of 1 item purchased? (A) 2.784 +- 12.29(0.2265) (B) 2.784 +- 2.262(0.2265) (C) 2.784 +- 2.262(0.2265/sqrt11) (D) 1.882 +- 1.96(6.6854) (E) 1.882 +- 2.262(6.6854)
(B) 2.784 +- 2.262(0.2265)
16. The transportation department of a large city wants to estimate the proportion of residents who would use a system of aerial gondolas to commute to work. The gondolas would be part of the city's effort to relieve traffic congestion. The department asked a random sample of residents whether they would use the gondolas. The residents could respond with yes, no, or maybe. Which of the following is the best description of the method for data collection used by the department? (A) A census (B) A sample survey (C) An experiment with a completely randomized design (D) An experiment with a randomized block design (E) An experiment with a matched-pairs design
(B) A sample survey
18. New employees at a large corporation go through a training program during their first week of employment. The new employees take a written assessment at the completion of the program to determine how well prepared they are for their jobs. A score greater than the mean indicates a well-prepared employee. Assume the following distributions of new employee scores have the same mean score, the same maximum score, and the same minimum score. Which distribution has a shape that is most likely to represent the greatest percent of well-prepared employees? (A) The distribution of scores is skewed to the right. (B) The distribution of scores is skewed to the left. (C) The distribution of scores is bimodal and symmetric. (D) The distribution of scores is uniform. (E) The distribution of scores is approximately normal.
(B) The distribution of scores is skewed to the left.
39. A doctor uses a new diagnostic test to indicate whether a patient has a certain disease. The doctor will prescribe medication for the patient if the doctor believes the patient has the disease, as indicated by the diagnostic test. The situation is similar to using a null hypothesis and an alternative hypothesis to decide whether to prescribe the medication. The hypotheses can be stated as follows. Ho : The patient does not have the disease. Ha : The patient has the disease. Which of the following best describes the power of the test? (A) The probability that the new test is better than an older test to indicate whether a patient has the disease (B) The probability that the new test indicates the disease in a patient who has the disease (C) The probability that the new test indicates the disease in a patient who does not have the disease (D) The probability that the new test does not indicate the disease in a patient who has the disease (E) The probability that the new test does not indicate the disease in a patient who does not have the disease
(B) The probability that the new test indicates the disease in a patient who has the disease
26. A company produces millions of 1-pound packages of bacon every week. Company specifications allow for no more than 3 percent of the 1-pound packages to be underweight. To investigate compliance with the specifications, the company's quality control manager selected a random sample of 1,000 packages produced in one week and found 40 packages, or 4 percent, to be underweight. Assuming all conditions for inference are met, do the data provide convincing statistical evidence at the significance level of a@ = 0.05 that more than 3 percent of all the packages produced in one week are underweight? (A) Yes, because the sample estimate of 0.04 is greater than the company specification of 0.03. (B) Yes, because the p-value of 0.032 is less than the significance level of 0.05. (C) Yes, because the p-value of 0.064 is greater than the significance level of 0.05. (D) No, because the p-value of 0.032 is less than the significance level of 0.05. (E) No, because the p-value of 0.064 is greater than the significance level of 0.05.
(B) Yes, because the p-value of 0.032 is less than the significance level of 0.05.
36. The president of a large company recommends that employees perform, on average, 24 hours of community service each year. The president believes that the mean number of hours of community service performed last year was different from the recommended 24 hours. To estimate the mean number of hours of community service performed last year, the president obtained data from a random sample of employees and used the data to construct the 95 percent confidence interval (20.37, 23.49). If all conditions for inference were met, does the interval provide convincing statistical evidence, at a level of significance of a = 0.05, to support the president's belief that the mean number of hours of community service performed last year is different from what is recommended? (A) Yes, the interval supports the president's belief because 0 is not contained in the interval. (B) Yes, the interval supports the president's belief because 24 is not contained in the interval. (C) No, the interval does not support the president's belief because a 90% confidence interval is required for a 5% level of statistical evidence. (D) No, the interval does not support the president's belief because confidence intervals should only be used for. estimation and cannot provide convincing statistical evidence. (E) No, the interval does not support the president's belief because the significance level is equal to 1 minus the confidence level, indicating that the results are not convincing.
(B) Yes, the interval supports the president's belief because 24 is not contained in the interval.
25. The distribution of assembly times required to assemble a certain smartphone is approximately normal with mean 4.6 minutes and standard deviation 0.6 minute. Of the following, which is closest to the percentage of assembly times between 4 minutes and 5 minutes? (A) 34% (B) 41% (C) 59% (D) 68% (E) 95%
(C) 59%
28. Researchers conducted a study to investigate the effects of soft drink consumption on fat stored in muscle tissue. From a sample of 80 adult volunteers, 40 were randomly assigned to consume one liter of a soft drink each day. The remaining 40 were asked to drink one liter of water each day and not to consume any soft drinks. At the end of six months, the amount of fat stored in each person's muscle tissue was recorded. The people in the group who drank the soft drink had, on average, a higher percentage of fat stored in the tissue than the people who drank only water. Which of the following is the most appropriate conclusion? (A) There is evidence that consuming soft drinks causes more fat storage in muscle tissue than drinking only water, and the conclusion can be generalized to all adults. (B) There is evidence that consuming soft drinks causes more fat storage in muscle tissue than drinking only water, and the conclusion can be generalized to all people who consume soft drinks. (C) There is evidence that consuming soft drinks causes more fat storage in muscle tissue than drinking only water, and the conclusion can be generalized to adults similar to those in the study. (D) Although cause-and-effect cannot be established, there is an association between consuming soft drinks and fat storage in muscle tissue for the population of all adults. (E) Although cause-and-effect cannot be established, there is an association between consuming soft drinks and fat storage in muscle tissue for the population of all adults who consume soft drinks.
(C) There is evidence that consuming soft drinks causes more fat storage in muscle tissue than drinking only water, and the conclusion can be generalized to adults similar to those in the study.
23. A study will be conducted to examine a new medicine intended to reduce high blood pressure in adult men who have high blood pressure. As part of the study, a random sample of 40 men with high blood pressure will have their blood pressure measured, and then they will take the new medicine every day for one month. At the end of the month, their blood pressure will be measured again. Of the following, which is the best procedure to investigate whether there will be convincing statistical evidence of a change, on average, in blood pressure for men with high blood pressure who take the new medicine? (A) A one-sample z-test for a proportion (B) A two-sample z-test for a difference between proportions (C) A two-sample -test for the difference between two means (D) A matched-pairs t-test for a mean difference (E) A chi-square test of independence
(D) A matched-pairs t-test for a mean difference
30. A manufacturer of cell phone batteries claims that the average number of recharge cycles for its batteries is 400. A consumer group will obtain a random sample of 100 of the manufacturer's batteries and will calculate the mean number of recharge cycles. Which of the following statements is justified by the central limit theorem? (A) The distribution of the number of recharge cycles for the sample is approximately normal because the population mean of 400 is greater than 30. (B) The distribution of the number of recharge cycles for the sample is approximately normal because the sample size of 100 is greater than 30. (C) The distribution of the number of recharge cycles for the population is approximately normal because the sample size of 100 is greater than 30. (D) The distribution of the sample means of the number of recharge cycles is approximately normal because the sample size of 100 is greater than 30. (E) The distribution of the sample means of the number of recharge cycles is approximately normal because the population mean of 400 is greater than 30.
(D) The distribution of the sample means of the number of recharge cycles is approximately normal because the sample size of 100 is greater than 30.
22. As part of a study on facility needs, the administrators of a university wanted to estimate the percent of students who use the exercise facilities on a regular basis. From the 34,000 students who attend the university, a random sample of 370 male students and 400 female students was selected. Of the 770 students selected, 493 students indicated that they use the exercise facilities on a regular basis. What are the population and the sample of the study? (A) The population is the 770 students who were selected, and the sample is the 493 students who indicated that they use the exercise facilities on a regular basis. (B) The population is the 770 students who were selected, and the sample is whether each student in the survey uses the exercise facility on a regular basis. (C) The population is the 34,000 students who attend the university, and the sample is whether each student in the survey is male or female. (D) The population is the 34,000 students who attend the university, and the sample is the 770 students who were selected. (E) The population is the 34,000 students who attend the university, and the sample is the 493 students who indicated that they use the exercise facilities on a regular basis.
(D) The population is the 34,000 students who attend the university, and the sample is the 770 students who were selected.
34. According to a recent report, customers who shop at a certain online store spend, on average, $1,500 a year at the store. To investigate whether the mean amount spent was greater than the reported average, an economist obtained the mean and standard deviation of the amount spent in the past year by a random sample of 120 customers who shop at the store. With all conditions for inference met, the economist conducted the appropriate hypothesis test and obtained a p-value of 0.25. Which of the following statements is the most appropriate conclusion for the investigation? (A) There is convincing statistical evidence that the mean amount of money spent each year by all customers who shop at the store is $1,500. (B) There is convincing statistical evidence that the mean amount of money spent each year by all customers who shop at the store is greater than $1,500. (C) There is convincing statistical evidence that the mean amount of money spent each year by all customers who shop at the store is less than $1,500. (D) There is not convincing statistical evidence that the mean amount of money spent each year by all customers who shop at the store is greater than $1,500. (E) There is not convincing statistical evidence that the mean amount of money spent each year by any sample of 120 customers who shop at the store is greater than $1,500.
(D) There is not convincing statistical evidence that the mean amount of money spent each year by all customers who shop at the store is greater than $1,500.
29. A random sample of 1,018 city residents were asked to rate their level of support for a proposal being considered by the city council. The table shows the responses by level of support. Based on the responses, which of the following is a 95 percent confidence interval for the proportion of all city residents who would respond very supportive or somewhat supportive of the proposal? (A) 0.33 +- 0.029 (B) 0.38 +- 0.030 (C) 0.71 +- 0.058 (D) 0.71 +- 0.031 (E) 0.71 +- 0.028
(E) 0.71 +- 0.028
32. A fitness center offers a one-month program designed to reduce body fat through exercise. The table shows the body fat percentage before and after completing the program for 10 randomly selected participants. The director of the program wants to investigate whether knowing the body fat percentage before beginning the program can help to predict body fat percentage for someone who completes the program. Which of the following procedures is the most appropriate for such an investigation? (A) A matched-pairs t-test for a mean difference (B) A two-sample t-test for a difference between means (C) A two-sample z-test for a difference between proportions (D) A chi-square test of association (E) A linear regression t-test for slope
(E) A linear regression t-test for slope
33. A recent survey estimated that 19 percent of all people living in a certain region regularly use sunscreen when going outdoors. The margin of error for the estimate was 1 percentage point. Based on the estimate and the margin of error, which of the following is an appropriate conclusion? (A) Approximately 1% of all the people living in the region were surveyed. (B) Between 18% and 20% of all the people living in the region were surveyed. (C) All possible samples of the same size will result in between 18% and 20% of those surveyed indicating they regularly use sunscreen. (D) The probability is 0.01 that a person living in the region will use sunscreen when going outdoors. (E) It is plausible that the percent of all people living in the region who regularly use sunscreen is 18.5%.
(E) It is plausible that the percent of all people living in the region who regularly use sunscreen is 18.5%.
21. For a school fund-raiser, 600 raffle tickets were sold by students at the school, of which 88 were sold by one student, Audrey. Of the 600 tickets sold, 30 were randomly selected to receive prizes, and 7 of the 30 tickets selected were tickets sold by Audrey. To investigate how likely it was by chance alone that at least 7 of the 30 selected tickets could have been sold by Audrey, students in a statistics class ran a simulation. One trial of the simulation is described by the following steps. Step 1: From 600 chips, assign 88 red and the rest blue. Step 2: Select 30 chips at random without replacement. Step 3: Record the number of red chips in the selection of 30. Based on the results of the simulation, is there convincing statistical evidence at the significance level of 0.05 that the event of Audrey selling at least 7 of the 30 selected tickets is unlikely to have occurred by chance alone? (A) Yes, because the distribution of the trials in the simulation is skewed to the right. (B) Yes, because the number in the histogram with the greatest frequency is 4, not 7. (C) Yes, because 7 appears in the right tail of the distribution, indicating that it is more than 2 standard deviations away from the mean. (D) No, because the simulation suggests that it is likely that Audrey could sell anywhere from 0 to 11 of the selected tickets. (E) No, because the simulation suggests that Audrey selling at least 7 of 30 selected tickets would occur about 13.8% of the time.
(E) No, because the simulation suggests that Audrey selling at least 7 of 30 selected tickets would occur about 13.8% of the time.
14. A pharmaceutical company manufactures medicine to reduce pain caused by migraine headaches. The company is investigating whether a new medicine is more effective in reducing pain than the current medication. A random sample of 500 participants who experience migraines was selected, and the participants were randomly assigned to one of the two groups of equal size. The first group received the current medicine and the second group received the second medicine. When a participant got a migraine, they were instructed to take the medicine and, 15 minutes after taking the medicine, to rate the pain relief on a scale from 1 to 10, 1=no relief, 10=complete relief. At the end of the 6 months, the average pain relief for each participant was calculated. Which of the following is a description of the study. A) An experiment using a completely randomized design B) An experiment using a matched-pairs design C) An observational study using a simple random sample D) An observational study using a cluster sample. E) An observational study using a stratified sample.
A) An experiment using a completely randomized design
17. To obtain certification for a certain occupation, candidates take a proficiency exam..The exam consists of two sections, and neither section should be more difficult than the other. To investigate whether one section of the exam was more difficult than the other, a random sample of 50 candidates was selected. The candidates took the exam and their scores on each section were recorded. The table shows the summary statistics. Which of the following is the test statistic for the appropriate test to determine if there is a significant mean difference between the percent correct on the two sections (first minus second) for all candidates similar to those in the investigation?
A. T=75-65/(8/sqrt(50))
11. A sociologist collected data from a sample of people on their highest level of education and the number of times they visited any fast food restaurant during the previous week. The data are summarized in the boxplots. Based on the boxplots, which of the following statements must be true? A) The number of people surveyed at the more than 4 year college level is greater than the number of people surveyed at the high school level. B) The proportion of people surveyed from the first quartile to the third quartile at the 4 year college level is less than the respective proportion at the community college level. C) The interquartile range (IQR) for the number of visits at the more than 4 year college level is less than the IQR for the number of visits at the community college level. D) The maximum number of visits at the community college level is greater than the maximum number of visits at the high school level. E) The median number of visits at the 4 year college level is greater than the median number of visits at the high school level.
C) The interquartile range (IQR) for the number of visits at the more than 4 year college level is less than the IQR for the number of visits at the community college level.
7. Nyasha's financial literacy project involved comparing the annual sales of companies in Canada and companies in the US that produce software. Using the ratio of 1 CAD to 0.75 USD, she converted all annual sales from the Canadian companies into United States dollars. For which of the following will the value of statistics for the annual sales in Canadian dollars be equal to the value of the corresponding statistic in US dollars? A) The median annual sales B) The standard deviation of annual sales C) The standardized score of the minimum annual sales D) The mean annual saless E) The interquartile range of the annual sales
C) The standardized score of the minimum annual sales
A company that makes fleece clothing uses fleece produced from two farms, Northern Farm and Western Farm. Let the random variable X represent the weight of fleece produced by a sheep from Northern Farm. The distribution of X has a mean 14.1 pounds and a standard deviation 1.3 pounds. Let the random variable Y represent the weight of fleece produced by a sheep from Western Farm. The distribution of Y has a mean 6.7 pounds and a standard deviation of 0.5 pounds. Assume X and Y are independent. Let W equal the total weight of fleece from 10 randomly selected sheep from Northern Farm and 15 randomly selected sheep from Western Farm. Which of the following is the standard deviation, in pounds, of W? A) 1.3+0.5 B) sqrt(1.3^2+0.5^2) C) sqrt(10(1.3)^2+15(0.5)^2) D) sqrt(10^2(1.3)^2+15^2(0.5)^2) E) sqrt((1.3)^2/10 + (0.5)^2/15
C) sqrt(10(1.3)^2+15(0.5)^2)
15. A marketing firm obtained random samples of 20 people in five regions of the country to investigate the level of interest in a new product. People in the same were asked to rate their level of interest on a scale from 1 to 10, with 1 being the least amount of interest and 10 being the greatest. The histograms show the results for each region. The graph for which region displays data for level of interest with the least standard deviation?
D)
1. The histogram summarizes the responses of 100 people when asked,"What was the price of the last meal you purchased?" Based on the histogram, which of the following could be the interquartile range of the prices? A) $40 B) $21 C) $10 D) $5 E) $3
D) $5
3. A veterinarian collected data on the weights of 1,000 cats and dogs treated at a veterinary clinic. The weight of each animal was classified as either healthy, underweight, or overweight. The data are summarized in the table. Based on the data in the table, which of the following is the appropriate type of graph to visually show whether a relationship exists between the type of animal and the weight classification. A) Back-to-back stemplots B) Scatterplot C) Side-by-side boxplots D) Segmented bar chart E) Dotplot
D) Segmented bar chart
10. According to a report for veterinarians in the United States, 36.5 percent of households in the United States own dogs and 30.4 percent of households in the United States own cats. If one household in the United States is selected at random, what is the probability that the selected household will own a dog or a cat? A) 0.111 B) 0.331 C) 0.558 D) 0.669 E) Not enough information is given to determine the probability.
E) Not enough information is given to determine the probability.
8. The manager of a restaurant tracks the types of dinners that customers order from the menu to ensure that the correct amount of food is ordered from the supplier each week. Data from customer orders last year suggest the following weekly distribution. The manager believes that there might be a change in the distribution from last year to this year. A random sample of 200 orders was taken from all customer orders placed last week. The following table shows the results of the sample. Assume each order is independent. For which type of dinner is the value of its contribution to the appropriate test statistic the greatest? A) Beef B) Chicken C) Fish D) Pork E) Vegetarian
E) Vegetarian
20. A medical center conducted a study to investigate cholesterol levels in people who have had heart attacks. A random sample of 16 people was obtained from the names of all patients of the medical center who had a heart attack in the previous year. Of the people in the sample, the mean cholesterol level was 264.70 milligrams per deciliter (mg/dL) with standard deviation 42.12 mg/dL. Assuming all conditions for inference were met, which of the following is a 90 percent confidence interval for the mean cholesterol level, in mg/dL, of all patients of the medical center who had a heart attack in the previous year? (A) (242.26, 287.14) (B) (244.06, 285.34) (C) (246.24, 283.16) (D) (247.38, 282.02) (E) (260.09, 269.31)
(C) (246.24, 283.16)
31. A news organization conducted a survey about preferred methods for obtaining the news. A random sample of 1,605 adults living in a certain state was selected, and 16.2 percent of the adults in the sample reported that television was their preferred method. Which of the following is an appropriate margin of error for a 90 percent confidence interval to estimate the population proportion of all adults living in the state who would report that television is their preferred method for obtaining the news?
A. 1.645sqrt((0.162(1-0.162)/1,605)
13. First year students enrolled at a college were asked whether they play video games. The responses, classified by whether the students were enrolled in the school of sciences or the school of arts are shown in the table. Of all the students enrolled in the school of arts who responded, approximately what proportion responded that they play video games. A) 0.242 B) 0.401 C) 0.438 D) 0.554 E) 0.605
C) 0.438
12. For a recent season in college football, the total number of rushing yards for that season is recorded for each running back. The mean number of rushing yards for the running backs that season is 790 yards. One running back had 1,637 rushing yards for the season, which is 2.42 standard deviations above the mean number of rushing yards. What is the standard deviation of the number of rushing yards for the running backs that season? A) 250 yards B) 300 yards C) 350 yards D) 400 yards E) 450 yards
C) 350 yards
2. Suppose a certain scale is not calibrated correctly, and as a result, the mass of any object is displayed as 0.75 kilogram less that its actual mass. What is the correlation between the actual masses of a set of objects and the respective masses of the same set of objects displaced by the scale? A) -1 B) -0.75 C) 0 D) 0.75 E) 1
E) 1
5. The normal curve shown represents the sampling distribution of a sample mean for a sample size n=25, selected at random from a population with a standard deviation Ox. Which of the following is the best estimate of the standard deviation of the population, Ox? A) 3 B) 6 C) 15 D) 30 E) 75
E) 75
19. Based on his past record, Luke, an archer for a college archery team, has a probability of 0.90 of hitting the inner ring of the target with a shot of the arrow. Assume that in one practice Luke will attempt 5 shots of the arrow and that each shot is independent from the others. Let the random variable X represent the number of times he hits the inner ring of the target in 5 attempts. The probability distribution of X is given in the table. What is the probability that the number of times Luke will hit the inner ring of the target out of the 5 attempts is less than the mean of X ? (A) 0.40951 (B) 0.50000 (C) 0.59049 (D) 0.91854 (E) 0.99144
(A) 0.40951
27. The histograms show the results of three simulations of a sampling distribution of a sample mean. For each simulation, 1,500 samples of size n were selected from the same population and the sample mean was recorded. The value of n was different for each of the three simulations. Which of the following is the correct ordering of the graphs from least value of n to greatest value of n? (A) A, C, B (B) B, A, C (C) B,C, A (D) C, A, B (E) C,B,A
(A) A, C, B
24. A roadrunner is a desert bird that tends to run instead of fly. While running, the roadrunner uses its tail as a balance. A sample of 10 roadrunners was taken, and the birds' total length, in centimeters (cm), and tail length, in cm, were recorded. The output shown in the table is from a least-squares regression to predict tail length given total length. Suppose a roadrunner has a total length of 59.0 cm and tail length of 31.1 cm. Based on the residual, does the regression model overestimate or underestimate the tail length of the roadrunner? (A) Underestimate, because the residual is positive. (B) Underestimate, because the residual is negative. (C) Overestimate, because the residual is positive. (D) Overestimate, because the residual is negative. (E) Neither, because the residual is 0.
(A) Underestimate, because the residual is positive.
6. Two random samples, A and B, were selected from the same population to estimate the population mean. For each sample, the mean, standard deviation, and margin of error for a 95 percent confidence interval for the population mean are show in the table. Which of the following could explain why the margin of error of sample A is greater than the margin of error of Sample B? A) The sample size of A is greater than the sample size of B. B) The sample size of A is less than the sample size of B. C) The sample size of A is equal to the sample size of B. D) The mean of sample A is greater than the mean of sample B. E) The standard deviation of sample A is less than the standard deviation of sample B.
B) The sample size of A is less than the sample size of B.
