(Chapters 1-9) 2. Following is a histogram of home sale prices (in thousands of dollars) in one community:

Transcription

1 (Chapters 1-9) 1. The boxplots below summarize the distributions of SAT verbal and math scores among students at an upstate New York high school. Which of the following statements are true? I. The range of the math scores equals the range of the verbal scores. II. The highest math score equals the median verbal score. III. The verbal scores appear to be roughly symmetric, while the math scores appear to be skewed to the right. (A) I only (B) III only (C) I and II (D) II and III (E) I, II, and III 2. Following is a histogram of home sale prices (in thousands of dollars) in one community: Which of the following statements are true? I. The median price was $125,000. II. More homes sold for between $100,000 and $125,000 than for over $125,000. III. $10,000 is a reasonable estimate of the standard deviation in selling prices. (A) I only (B) II only (C) III only (D) All are true. (E) None is true. 3. One national test has a normal distribution with a mean of 500 and a standard deviation of 100, while a second test has a normal distribution with a mean of 18 and a standard deviation of 6. A student scored 677 on one test and 29 on the other. Relative to the respective distributions, which score is better? (A) The score of 677 is better. (B) The score of 29 is better. (C) The scores are equally strong. (D) A comparison cannot be made without knowing the number of students who took each exam. (E) It is improper to compare scores for the same student on different exams.

2 4. Which of the following can stemplots show? I. Symmetry II. Gaps III. Clusters IV. Outliers (A) I, II, and III (B) I, II, and IV (C) I, III, and IV (D) II, III, and IV (E) I, II, III, and IV 5. Which among the following is most useful in establishing cause-and-effect relationships? (A) A complete census (B) A least squares regression line showing high correlation (C) A simple random sample (SRS) (D) A well-designed, well-conducted survey incorporating chance to ensure a representative sample (E) A controlled experiment 6. A researcher plans a study to examine long term confidence in the U.S. economy among the adult population. She obtains a simple random sample of 30 adults as they leave a Wall Street building one weekday afternoon. All but two of them agree to participate in the survey. Which of the following is true? I. Proper use of chance as evidenced by the simple random sample makes this a well designed experiment. II. The high response rate makes this a well designed survey. III. Selection bias makes this a poorly designed survey. Which of the following statements is the most reasonable conclusion based on the above data? (A) I only (B) II only (C) III only (D) I and II (E) None of the statements listed above (I, II, III) are true 7. A cross-country coach who is also the school's AP Statistics teacher calculates that one runner, Bill, had a standardized score (z-score) of 1.6 for his time in a 5K event as compared to the entire group of runners in the race. Which of the following is the best interpretation of Bill's z-score? (A) Bill's time was 16 minutes. (B) Only 1.6% of the runners did better than Bill. (C) Bill's time is 1.6 times the average time of all the runners. (D) Bill's time is 1.6 minutes above the average time of all the runners. (E) Bill's time is 1.6 standard deviations above the average time of all the runners.

3 8. A histogram of the cholesterol levels of all employees at a large law firm is as follows: Which of the following is the best estimate of the standard deviation of this distribution? ( ) (A) = 10 6 (B) (C) = (D) = 60 (E) = The average yearly snowfall in a city is 55 inches. What is the standard deviation if 15% of the years have snowfalls above 60 inches? Assume yearly snowfalls are normally distributed. (A) 4.83 (B) 5.18 (C) 6.04 (D) 8.93 (E) The standard deviation cannot be computed from the information given. 10. The owners of a concession stand at a baseball field know that sales depend on weather conditions and use probabilities to estimate the numbers of hot dogs and soft drinks they will sell. The following tables summarize their estimations. Hot dog sales Soft drink sales Weather Hot Mild Cold Weather Hot Mild Cold Probability Probability # Sold 8,000 10,000 15,000 # Sold 20,000 15,000 5,000 If hot dogs sell for $3.00 and soft drinks for $1.25, what is the expected revenue over an 81-game home season? (A) $24,900 (B) $49,325 (C) $2,017,000 (D) $3,995,000 (E) $4,286, Suppose that a computer virus randomly infects 15% of the desktop computers at a large research center. Let X be the number of virus-free computers in a sample of four desktops. What is the most probable value of X? (A) 0 (B) 1 (C) 2 (D) 3 (E) 4

4 12. Which of the following data sets has the smallest standard deviation? Which one has the highest? I. 1,2,3,4,5,6,7 II. 1,1,1,4,7,7,7 III. 1,4,4,4,4,4,7 (A) I, II (B) II, III (C) III, I (D) II, I (E) III, II 13. There is a rough linear relationship between the number of assists and the number of steals by professional basketball players. A least squares fit results in the model ŷ = 0.52x , x 1, where x is the number of assists and ŷ is the estimated number of steals. What is the estimated increase in steals that corresponds to an increase of three assists? (A) 0.27 (B) 0.52 (C) 1.13 (D) 1.56 (E) The following are parts of the probability distributions for the random variables X and Y. X Y P(x).25?.35? P(y).3.5? If X and Y are independent and the joint probability P(X = 2, Y = 3) =.03, what is P(X = 4)? (A).10 (B).15 (C).20 (D).25 (E) A survey is to be taken to ascertain student opinions about the quality of teaching at a high school. Consider the following survey methods of picking 100 students out of the 2000 students registered at the school. I. Randomly pick one day of the week. As the students arrive at school that day, they are asked to write their names on slips of paper and place these slips in a box. The principal then reaches in and pulls out 100 names. II. Using an official school roster of the 2000 students, pick every 20th name. III. Using a random number table, 25 names are chosen from each of separate lists of freshmen, sophomores, juniors, and seniors. IV. Randomly pick 5 freshmen homerooms, 5 sophomore homerooms, 5 junior homerooms, and 5 senior homerooms. Then randomly pick 5 students from each of these 20 homerooms. How many of the above survey methods will result in a simple random sample of 100 students? (A) None (B) One (C) Two (D) Three (E) Four

5 16. A study on school budget approval among people with different party affiliations resulted in the following segmented bar chart: Which of the following is greatest? (A) Number of Democrats who are for the proposed budget (B) Number of Republicans who are against the budget (C) Number of Independents who have no opinion on the budget (D) The above are all equal. (E) The answer is impossible to determine without additional information. 17. In one study on the effect that eating meat products has on weight level, an SRS of 500 subjects who admitted to eating meat at least once a day had their weights compared with those of an independent SRS of 500 people who claimed to be vegetarians. In a second study, an SRS of 500 subjects were served at least one meat meal per day for 6 months, while an independent SRS of 500 others were chosen to receive a strictly vegetarian diet for 6 months, with weights compared after 6 months. (A) The first study is a controlled experiment, while the second is an observational study. (B) The first study is an observational study, while the second is a controlled experiment. (C) Both studies are controlled experiments. (D) Both studies are observational studies. (E) Each study is part controlled experiment and part observational study. 18. Skip! 19. Exams I, II, and III have mean results of 67, 72, and 76, respectively, and standard deviations of 11, 8, and 5, respectively. Mary takes exam I, John takes exam II, and Sarah takes exam III. They each score 83. Rank them from lowest to highest results according to z-scores. (A) John, Sarah, Mary (B) Mary, John., Sarah (C) Sarah, John, Mary (D) John, Mary, Sarah (E) Mary, Sarah., John 20. The Wechsler Adult Intelligence Scale results in a normal distribution with a mean of 110 and a standard deviation of 25. If someone tests at the 80th percentile, what score did that individual have? (A) 89 (B) 113 (C) 118 (D) 130 (E) 131

6 Questions refer to the following: A diner advertises that for the month of January the price of soup in cents will be the temperature at 10 A.M. that morning. If the 10 A.M. temperature is 20 degrees Fahrenheit, soup will sell for 20 cents a cup! The store owner, whose hobby is statistics, notes that the temperatures seem normally distributed and calculates that the expected value of a cup of soup any day in January is 28 cents with a standard deviation of 7 cents. Suppose a customer buys a cup of soup on ten random days in January. (Assume the temperature on any day is independent of the temperature on any other day, which is probably an unreasonable assumption!) 21. What is the total amount the customer should expect to pay? (A) $2.10 (B) $2.45 (C) $2.80 (D) $3.15 (E) $ What is the approximate probability that the total amount the customer pays will exceed $3.00? (A).06 (B).18 (C).28 (D).39 (E) There are 16,253 men and 21,784 women at a large state university. If 28% of the men and 44% of the women are social science majors, what is the expected number of social science majors in a random sample of 100 students? (A) 28 (B) 36 (C) 37 (D) 44 (E) A test is run to compare two calculus textbooks, one with a traditional approach and one with a reform approach. A state university agrees to use the traditional text in all of its 30 classes, each with approximately 50 students. A private liberal arts college agrees to use the reform text in its 4 calculus classes, each with 20 students. An SRS of 30 calculus students at each school will take a standardized final exam, and the mean scores of the two groups will be compared. Is this a good experimental design? (A) Yes. (B) No, because proportions of students passing would be the more appropriate variable. (C) No, because the standardized exam should have been given to all the calculus students. (D) No, because so many more students take calculus at the university than at the college. (E) No, because there is a confounding variable: large public university versus small private college. 25. Given the probabilities P (A) =.3 and P (B) =.2, what is the probability of the union P (A B) if A and B are mutually exclusive? If A and B are independent? If B is a subset of A? (A).44,.5,.2 (B).44,.5,.3 (C).5,.44,.2 (D).5,.44,.3 (E) 0,.5,.3

7 26. A study is made to determine whether more hours of academic studying leads to higher point scoring by basketball players. In surveying 50 basketball players, it is noted that the 25 who claim to study the most hours have a higher point average than the 25 who study less. Based on this study, the coach begins requiring the players to spend more time studying. Which of the following are true statements? I. While this study indicates a relation, it does not prove causation. II. There could well be a confounding variable responsible for the seeming relationship. III. While this is a controlled experiment, the conclusion of the coach is not justified. (A) I only (B) I and II (C) I and III (D) II and III (E) I, II, and III 27. The distribution of blood cholesterol levels among females between 30 and 40 years old is roughly normal. If 10% have levels above 238 and 20% have levels below 187, what is the mean of this distribution? (A) (B) (C) (D) (E) The mean cannot be calculated from the given information. 28. One-third of retired senior executives return to work within 1.5 years of retirement. According to Russel Reynolds Association, the reasons for and path of return are as follows: Reasons for returning: Job satisfaction Avoid boredom Contribute to society Probability: Employed by How they returned: another company Self-employed Consultant Started a new company Probability: Assuming reasons and path are independent, what is the probability that a retired senior executive will decide to return to work, the reason being to avoid boredom, on a path as a consultant? (A).0222 (B).0667 (C).1733 (D).5200 (E) Which of the following can affect the value of the correlation r? (A) A change in measurement units (B) A change in which variable is called x and which is ca1led y (C) Adding the same constant to all values of the x-variable (D) All of the above can affect the r value. (E) None of the above can affect the r value.

8 30. A reporter from a consumer magazine notes that the mean price of 30 selected grocery items at a particular supermarket is $0.75 with a standard deviation of $0.20. Suppose the following week the store raises all prices by 5 cents, and then the next week they lower all prices by 5%. What are the new mean and standard deviation for the 30 selected items? (A) $0.76, $0.19 (B) $0.76, $0.20 (C) $0.76, $0.24 (D) $0.80, $0.20 (E) $0.80, $0.24 Questions refer to the following: In a general market survey of buying habits, 15,000 out of 50,000 town residents are identified as purchasers of vitamin supplements. 31. In an SRS of five town residents, what is the expected value for the number who purchase vitamin supplements? (A) 0.3 (B) 1.0 (C) 1.5 (D) 2.0 (E) Which of the following statements about residuals are true? I. The mean of the residuals is always zero. II. Influential scores have large residuals III. A definite pattern in the residual plot is an indication that a nonlinear model should be tried. (A) II only (B) I and III (C) I and III (D) II and III (E) I, II and III 33. According to one poll, 12% of the public favor legalizing all drugs. In a simple random sample of six people, what is the probability that at least one person favors legalization? (A).380 (B).464 (C).536 (D).620 (E).844

9 34. Treatment of breast cancer is a controversial issue with treatment varying from radical mastectomy to radiation and chemotherapy combined with simple lumpectomy. One long-term study involved noting survival times of all breast cancer patients from over 100 hospitals and comparing the percentage of women still alive 5 years after radical mastectomies with the percentage of women still alive 5 years after radiation and chemotherapy combined with simple lumpectomy. The results seemed to show a better outcome for women who received lumpectomy treatment. Which of the following statements are appropriate? I. This appears to be a well-conducted controlled experiment. II. This observational study should be faulted for a lack of blinding. III. A lurking variable involving who received what treatment makes any conclusion suspect. (A) I only (B) II only (C) III only (D) I and II (E) II and III 35. Consider the following three scatterplots: What is the relationship among r 1, r 2, and r 3, the correlations associated with the first, second, and third scatterplots, respectively? (A) r 1 < r 2 < r 3 (B) r 1 < r 3 < r 2 (C) r 2 < r 3 < r 1 (D) r 3 < r 1 < r 2 (E) r 3 < r 2 < r The least squares regression line for a scatterplot is ŷ = 0.61x What is the residual for the point (3, 1)? (A) (B) (C) (D) (E) There are two games involving flipping a coin. In the first game you win a prize if you can throw between 45% and 55% heads. In the second game you win if you can throw more than 80% heads. For each game would you rather flip the coin 30 times or 300 times? (A) 30 times for each game (B) 300 times for each game (C) 30 times for the first game and 300 times for the second (D) 300 times for the first game and 30 times for the second (E) The outcomes of the games do not depend on the number of flips

10 38. The back-to-back stemplot below give the average bowling scores of male and female participants in the finals of a national tournament. Males Females Which of the following is not true? (A) The same number of male and female bowlers participated. (B) The male scores are skewed while the female scores are roughly symmetric. (C) The median and mean female scores are roughly equal. (D) The mean male score is greater than the median male' score. (E) The range of the male scores equals the range of the. female scores. Questions refer to the following calculator output: LinReg y =ax+b a = b = r = where x is the yearly liters per person of alcohol from wine consumption and y is the yearly deaths per 100,000 people from heart disease for a sample of countries. 39. For every additional liter per person of alcohol from wine consumption, what is the anticipated change in heart disease deaths per 100,000 people? (A) 24 fewer (B) 27 more (C) 87 fewer (D) 267 more (E) 267 fewer 40. What fraction of the difference in heart disease deaths per 100,000 people among various countries can be explained by differences in wine consumption among those countries? (A) 8.7% (B) 23.8% (C) 63.5% (D) 76.2% (E) 87.3%