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4/11/17 AP Statistics Partner Activity Chapters 10, 11 Calculators are always allowed in AP Stats! Statisticians: 1. A survey was conducted in which both men and women were asked a question about a current issue. Possible responses to this question were “in favor of,” “not in favor of,” or “no opinion.” A chi-square test is to be used to determine whether the response to this question is independent of gender. the number of degrees of freedom for the chi-square test in this situation is A. 6 B. 5 C. 3 D. 2 E. 1 2. Makers of a new pain-relieving medication claim that it relieves chronic pain faster than the current topselling pain reliever on the market. a double-blind experiment was conducted in which 10 people who experience chronic pain were randomly selected to take either the new or the current medication. Each of the 10 people recorded the time, in minutes, from taking the medication until pain relief. After an appropriate time period, each of the 10 people took the other medication and recorded the time from taking the medication until pain relief. The medication each person took first was randomly determined, and because both medications look the same, the people in the study did not know which medication was taken first. The table below shows summary statistics for the results. Minutes until Pain Relief New Medication Mean 15.6000 Standard deviation 4.811 Difference Current Medication (new – current) 16.025 -0.425 4.833 1.395 Which of the following is closest to the p-value of the appropriate test? A. 0.1802 B. 0.3604 C. 0.4230 D. 0.5770 E. 0.8198 3. In an experiment testing whether a new feed increased mean weight gain when compared to an old feed, it was found that the new feed gave a 10 kg bigger weight gain than the old feed. A two –sample t-test with the proper one-sided alternative was done and the resulting p-value was 0.082. This means that: A. There is an 8.2% chance the null hypothesis is true. B. There was only an 8.2% chance of observing an increase greater than 10 kg, assuming the null hypothesis was true. C. There was only an 8.2% chance of observing an increase greater than 10 kg, assuming the null hypothesis was false. D. There is an 8.2% chance the alternate hypothesis is true. E. There is only an 8.2% chance of getting a 10 kg weight increase. 4. An SRS of 25 male faculty members at a large university found that 10 felt that the university was supportive of female and minority faculty. An independent SRS of 20 female faculty found that five felt that the university was supportive of female and minority faculty. Let p1 represent the proportion of all male faculty members at the university and p2 represent the proportion of all female faculty members at the university who hold the stated opinion. A 95% confidence interval for p1 – p2 = A. 0.15 0.355 B. 0.15 0.270 D. 0.15 0.138 C. 0.15 0.227 E. 0.15 0.168 5. The following two way table resulted from classifying each individual in a random sample of residents of a small city according 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”). Earned at least a high school diploma Did not earn a high school diploma Total Employed full time Not employed full time Total 52 40 92 30 35 65 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 time? A. (92)(52) 157 D. B. (92)(82) 157 (65)(52) 92 C. E. (82)(52) 157 (92)(52) 82 6. The manager of a factory wants to compare the mean number of units assembled per employee in a week for two new assembly techniques. Two hundred employees from the factory are randomly selected and each is randomly assigned to one of the two techniques. After teaching 100 employees one technique one technique and 100 employees the other technique, the manager records the number of units each of the employees assemble in one week. Which of the following would be the most appropriate inferential statistical test in this situation? A. one-sample z-test B. two-sample t-test D. chi-square goodness-of-fit test C. paired t-test E. one-sample t-test 7. A marketing research consultant for a hotel chain hypothesizes that men and women differ in their color preference for guest rooms. The consultant shows pictures of rooms decorated with three different color schemes to each person in a random sample of 110 men and to each person in a random sample of 90 women. The consultant asks each person to choose his or her favorite color scheme. A chi-square test for homogeneity of proportions will be used to test the consultant’s hypothesis. Assuming that the conditions for inference are met, which of the following statements is true for the test? A. The null hypothesis for the test is that the proportion of each gender who prefer each color scheme is 1 . 3 B. The sample size is too small to detect a significant difference in a chi-square test for homogeneity of proportions. C. The test is not valid because the sample sizes are not equal. D. The more that men and women differ in their color preferences, the larger the chi-square statistic will be. E. The test would also be appropriate if 90 married couples had been used for the two samples. 8. (2014 #5 secure) The newspaper staff at a large high school randomly sampled students at the school to investigate the relationship between choice of favorite sport to watch and gender. Students in the sample were asked the following question: Of the following five sports, which one is your favorite to watch: baseball, basketball, football, gymnastics, or swimming? The number of responses by choice of favorite sport to watch and gender were tabulated. The graph below displays the relative frequencies of each sport by gender. A. Write a few sentences summarizing what the graph reveals about the association between choice of favorite sport to watch and gender for the students in the sample. B. What statistical test should be used to investigate whether there is an association between choice of favorite sport to watch and gender for the population of students at the high school? What is the appropriate number of degrees of freedom the test should be based on? C. The conditions for inference were determined to be satisfied, and the appropriate statistical test was conducted. The value of the test statistic is 10.77. Is there convincing statistical evidence, at the 0.05 significance level, of an association between choice of favorite sport to watch and gender for all students at the high school? 9. (2014 #3 secure) Patients exhibiting symptoms of a heart attack are routinely transported to a hospital in an ambulance. In a study of a new treatment thought to reduce damage to the heart, patients experiencing symptoms of a heart attack were randomly assigned to one of two groups. During transportation to the hospital, patients in one group received standard care, and patients in the other group received the new treatment consisting of standard care and the application of a blood pressure cuff. The response variable measured for each patient was a number between 0 and 1, referred to as the myocardial salvage index (MSI). A higher MSI value indicates a more positive outcome for the patient. Summary statistics for the MSI responses of the two groups are shown in the table. Do the data provide convincing statistical evidence that the new treatment results in a higher mean MSI value than does the standard care among people similar to the patients in the study. Your signatures below indicate your adherence to both the letter and the spirit of the Honor Code. Grade ____/15