1、2002 AP 真题 1 STATISTICS SECTION I Time 90 minutes Number of questions 40 Percent of total grade 50 FORM A Directions: Solve each of the following problems, using the available space for scratchwork. Decide which is the best of the choices given and fill in the corresponding oval on the answer sheet.
2、 No credit will be given for anything written in the test book. Do not spend too much time on any one problem. 1. Which of the following is a key distinction between well designed experiments and observational studies? (A) More subjects are available for experiments than for observational studies. (
3、B) Ethical constraints prevent large-scale observational studies. (C) Experiments are less costly to conduct than observational studies. (D) An experiment can show a direct cause-and-effect relationship, whereas an observational study cannot. (E) Tests of significance cannot be used on data collecte
4、d from an observational study. 2. Lauren is enrolled in a very large college calculus class. On the first exam, the class mean was 75 and the standard deviation was 10. On the second exam, the class mean was 70 and the standard deviation was 15. Lauren scored 85 on both exams. Assuming the scores on
5、 each exam were approximately normally distributed, on which exam did Lauren score better relative to the rest of the class? (A) She scored much better on the first exam. (B) She scored much better on the second exam. (C) She scored about equally well on both exams. (D) It is impossible to tell beca
6、use the class size is not given. (E) It is impossible to tell because the correlation between the two sets of exam scores is not given. 2002 AP 真题 2 3. The number of sweatshirts a vendor sells daily has the following probability distribution. Number of Sweatshirts x 0 1 2 3 4 5 )(xP 0.3 0.2 0.3 0.1
7、0.08 0.02 If each sweatshirt sells for $25, what is the expected daily total dollar amount taken in by the vendor from the sale of sweatshirts? (A) $5.00 (B) $7.60 (C) $35.50 (D) $38.00 (E) $75.00 4. Suppose that the distribution of a set of scores has a mean of 47 and a standard deviation of 14. If
8、 4 is added to each score, what will be the mean and the standard deviation of the distribution of new scores? Mean Standard Deviation (A) 51 14 (B) 51 18 (C) 47 14 (D) 47 16 (E) 47 18 5. A volunteer for a mayoral candidates campaign periodically conducts polls to estimate the proportion of people i
9、n the city who are planning to vote for this candidate in the upcoming election. Two weeks before the election, the volunteer plans to double the sample size in the polls. The main purpose of this is to (A) reduce nonresponse bias (B) reduce the effects of confounding variables (C) reduce bias due t
10、o the interviewer effect (D) decrease the variability in the population (E) decrease the standard deviation of the sampling distribution of the sample proportion 2002 AP 真题 3 6. The following two-way table resulted form classifying each individual in a random sample of residents of a small city acco
11、rding to level of education (with categories “earned at least a high school diploma” and “did not earn a high school diploma”) and employment status (with categories “employed full time” and “not employed full time”). Employed full time Not employed full time Total Earned at least a high school dipl
12、oma 52 40 92 Did not earn a high school diploma 30 35 65 Total 82 75 157 If the null hypothesis of no association between level of education and employment status is true, which of the following expressions gives the expected number who earned at least a high school diploma and who are employed full
13、 time? (A) 1575292 (B) 1578292 (C) 925282 (D) 925265 (E) 825292 7. A random sample has been taken from a population. A statistician, using this sample, needs to decide whether to construct a 90 percent confidence interval for the population mean or a 95 percent confidence interval for the population
14、 mean. How will these intervals differ? (A) The 90 percent confidence interval will not be as wide as the 95 percent confidence interval. (B) The 90 percent confidence interval will be wider than the 95% confidence interval. (C) Which interval is wider will depend on how large the sample is. (D) Whi
15、ch interval is wider will depend on whether the sample is unbiased. (E) Which interval is wider will depend on whether a z-statistic or a t-statistic is used. 2002 AP 真题 4 8. A high school statistics class wants to conduct a survey to determine what percentage of students in the school would be will
16、ing to pay a fee for participating in after-school activities. Twenty students are randomly selected from each of the freshman, sophomore, junior and senior classes to complete the survey. This plan is an example of which type of sampling? (A) Cluster (B) Convenience (C) Simple random (D) Stratified
17、 random (E) Systematic 9. A least squared regression line was fitted to the weights (in pounds) versus age (in months) for a group of many young children. The equation of the line is where y is the predicted weight and t is the age of the child. A 20-month-old child in this group has an actual weigh
18、t of 25 pounds. Which of the following is the residual weight, in pounds, for this child? (A) -7.85 (B) -4.60 (C) 4.6 (D) 5.00 (E) 7.85 10. A geneticist hypothesizes that half of a given population will have brown eyes and the remaining half will be evenly split between blue- and green-eyed people.
19、In a random sample of 60 people from this population, the individuals are distributed as shown in the table above. What is the value of the 2 statistic for the goodness of fit test on these data? (A) Less than 1 (B) At least 1, but less than 10. (C) At least 10, but less than 20. (D) At least 20, bu
20、t less than 50. (E) At least 50. Brown Eyes Green Eyes Blue Eyes 34 15 11 ,65.06.16 ty 2002 AP 真题 5 11. In a study of the performance of a computer printer, the size (in kilobytes) and the printing time (in seconds) for each of 22 small text files were recorded. A regression line was a satisfactory
21、description of the relationship between size and printing time. The results of the regression analysis are shown below. Which of the following should be used to compute a 95 percent confidence interval for the slope of the regression line? (A) 294.0086.24 7 8 1 2.3 (B) 6 1 7 4.096.14 7 8 1 2.3 (C) 2
22、94.0725.14 7 8 1 2.3 (D) 3153.0086.26559.11 (E) 3 1 5 3.07 2 5.16 5 5 9.11 12. Which of the following statements is true for two events, each with probability greater than 0? (A) If the events are mutually exclusive, they must be independent. (B) If the events are independent, they must be mutually
23、exclusive. (C) If the events are not mutually exclusive, they must be independent. (D) If the events are not independent, they must be mutually exclusive. (E) If the events are mutually exclusive, they cannot be independent. 2002 AP 真题 6 13. A new medication has been developed to treat sleep-onset i
24、nsomnia (difficulty in falling asleep). Researchers want to compare this drug to a drug that has been used in the past by comparing the length of time it takes subjects to fall asleep. Of the following, which is the best method for obtaining this information? (A) Have subjects choose which drug they
25、 are willing to use, then compare the results. (B) Assign the two drugs to the subjects on the basis of their past sleep history without randomization, then compare the results. (C) Give the new drug to all subjects on the first night. Give the old drug to all subjects on the second night. Compare t
26、he results. (D) Randomly assign the subjects to two groups, giving the new drug to one group and no drug to the other group, then compare the results. (E) Randomly assign the subjects to two groups, giving the new drug to one group and the old drug to the other group, then compare the results. 14. T
27、he figure above shows a cumulative relative frequency histogram of 40 scores on a test given in an AP Statistics class. Which of the following conclusions can be made from the graph? (A) There is greater variability in the lower 20 test scores than in the higher 20 test scores. (B) The median test s
28、core is less than 50. (C) Sixty percent of the students had test scores above 80. (D) If the passing score is 70, most students did not pass the test. (E) The horizontal nature of the graph for test scores of 60 and below indicates that those scores occurred most frequently. 15. The analysis of a ra
29、ndom sample of 500 households in a suburb of a large city indicates that a 98 percent confidence interval for the mean family income is ($41,300, 2002 AP 真题 7 $58,630). Could this information be used to conduct a test of the null hypothesis 000,40: OH against the alternative hypothesis 000,40: aH at
30、 the 02.0 level of significance? (A) No, because the value of is not known. (B) No, because it is not known whether the data are normally distributed. (C) No, because the entire data set is needed to do this test. (D) Yes, since $40,000 is not contained in the 98 percent confidence interval, the nul
31、l hypothesis would be rejected in favor of the alternative, and it could be concluded that the mean family income is significantly different from $40,000 at the 02.0 level. (E) Yes, since $40,000 is not contained in the 98 percent confidence interval, the null hypothesis would not be rejected, and i
32、t could be concluded that the mean family income is not significantly different from $40,000 at the 02.0 level. 16. A wildlife biologist is interested in the relationship between the number of chirps per minute for crickets (y) and temperature. Based on the collected data, the least squares regressi
33、on line is xy 41.353.10 , where x is the number of degrees Fahrenheit by which the temperature exceeds 50 degrees. Which of the following best describes the meaning of the slope of the least squares regression line? (A) For each increase in temperature of 1 degree Fahrenheit, the estimated number of
34、 chirps per minute increases by 10.53. (B) For each increase in temperature of 1 degree Fahrenheit, the estimated number of chirps per minute increases by 3.41. (C) For each increase of one chirp per minute, there is an estimated increase in temperature of 10.53 degrees Fahrenheit. (D) for each incr
35、ease of one chirp per minute, there is an estimated increase in temperature of 3.41 degrees Fahrenheit. (E) The slope has no meaning because the units of measure for x and y are not the same. 17. An engineer for the Allied Steel Company has the responsibility of estimating the mean carbon content of
36、 a particular days steel output, using a random sample of 15 rods from that days output. The actual population distribution of carbon content is not known 2002 AP 真题 8 to be normal, but graphic displays of the engineers sample results indicate that the assumption of normality is not unreasonable. Th
37、e process is newly developed, and there are no historical data on the variability of the process. In estimating this days mean carbon content, the primary reason the engineer should use a t-confidence interval rather than a z-confidence interval is because the engineer (A) is estimating the populati
38、on mean using the sample mean (B) is using the sample variance as an estimate of the population variance (C) is using data, rather than theory, to judge that the carbon content is normal (D) is using data from a specific day (E) has a small sample, and a z-confidence interval should never be used wi
39、th a small sample 18. In a test of the hypothesis 100: OH versus 100: aH , the power of the test when 101 would be greatest for which of the following choices of sample size n and significance level ? (A) 05.0,100 n (correction, n = 10 and alpha = 0.05) (B) 01.0,10 n (C) 05.0,20 n (D) 01.0,20 n (E)
40、It cannot be determined from the information given. 19. A simple random sample produces a sample mean, x , of 15. A 95 percent confidence interval for the corresponding population mean is 315 . Which of the following statements must be true? (A) Ninety-five percent of the population measurements fal
41、l between 12 and 18. (B) Ninety-five percent of the sample measurements fall between 12 and 18. (C) If 100 samples were taken, 95 of the sample means would fall between 12 and 18. (D) 95.0)1812( xP (E) If 19 ,this x of 15 would be unlikely to occur. 20. As lab partners, Sally and Betty collected dat
42、a for a significance test. Both calculated the same z-test statistic, but Sally found the results were significant at the 05.0 level while Betty found that the results were not. When checking their results, the women found that the only difference in their work was that Sally had used a two-2002 AP
43、真题 9 sided test, wile Betty used a one-sided test. Which of the following could have been their test statistic? (A) -1.980 (B) -1.690 (C) 1.340 (D) 1.690 (E) 1.780 21. A manufacturer of balloons claims that p , the proportion of its balloons that burst when inflated to a diameter of up to 12 inches,
44、 is no more than 0.05. Some customers have complained that the balloons are bursting more frequently. If the customers want to conduct an experiment to test the manufacturers claim, which of the following hypotheses would be appropriate? (A) 05.0:,05.0: pHpH aO (B) 05.0:,05.0: pHpH aO (C) 05.0:,05.0
45、: pHpH aO (D) 05.0:,05.0: pHpH aO (E) 05.0:,05.0: pHpH aO 22. Suppose that 30 percent of the subscribers to a cable television service watch the shopping channel at least once a week. You are to design a simulation to estimate the probability that none of five randomly selected subscribers watches t
46、he shopping channel at least once a week. Which of the following assignments of the digits 0 through 9 would be appropriate for modeling an individual subscribers behavior in this simulation? (A) Assign “0, 1, 2” as watching the shopping channel at least once a week and “3, 4, 5, 6, 7, 8, and 9” as
47、not watching. (B) Assign “0, 1, 2, 3” as watching the shopping channel at least once a week and “4, 5, 6, 7, 8, and 9” as not watching. (C) Assign “1, 2, 3, 4, 5” as watching the shopping channel at least once a week and “6, 7, 8, 9, and 0” as not watching. (D) Assign “0” as watching the shopping ch
48、annel at least once a week and “1, 2, 3, 4, and 5” as not watching; ignore digits “6, 7, 8, and 9”. (E) Assign “3” as watching the shopping channel at least once a week and “0, 1, 2, 3, 4, 5, 6, 7, 8, and 9” as not watching. 23. The correlation between two scores X and Y equals 0.8. If both X scores
49、 and the Y scores are converted to z-scores, then the correlation between the z-scores for X and the z-scores for Y would be 2002 AP 真题 10 (A) -0.8 (B) -0.2 (C) 0.0 (D) 0.2 (E) 0.8 24. A test engineer wants to estimate the mean gas mileage (in miles per gallon) for a particular model of automobile. Eleven of these cars are subjected to a road test, and the gas mileage is computed for each car. A dotplot of the 11 gas-mileage values is roughly symmetrical and has no outliers. The mean
