One parameter of interest to the researchers is the

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Unformatted text preview: .11 0.69 Group Early birds Night owls (a) The researchers believe that night owls may have better dream recall than do early birds. One parameter of interest to the researchers is the mean number of dreams recalled per week with mE representing this mean for early birds and mN representing this mean for night owls. The appropriate hypotheses would then be H 0 : mE - mN = 0 and H a : mE - mN < 0. State two other pairs of hypotheses that might be used to test the researchers’ belief. Be sure to define the parameter of interest in each case. (b) Use the data provided to carry out a test of the hypotheses about the mean number of dreams recalled per week given in the statement of part (a). Do the data support the researchers’ belief ? Copyright © 2002 by College Entrance Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 9 GO ON TO THE NEXT PAGE. 2002 AP® STATISTICS FREE-RESPONSE QUESTIONS STATISTICS SECTION II Part B Question 6 Spend about 25 minutes on this part of the exam. Percent of Section II grade— 25 Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanation. 6. A survey given to a random sample of students at a university included a question about which of two wellknown comedy shows, S or F, students preferred. The students were asked the question, “Do you prefer S or F ?” The responses are shown below. Preference S F 185 139 Total 324 (a) Based on the results of this survey, construct and interpret a 95% confidence interval for the proportion of students in the population who would respond S to the question, “Do you prefer S or F ?” (b) What is the meaning of “95% confidence” in part (a) ? (c) In a follow-up survey, a separate group of randomly selected students was asked “Do you prefer F or S ?” The responses are shown below. Preference S F 68 88 Total 156 Based on these two surveys, is there evidence that the stated preference depends on the order in which the comedy shows were listed in the survey question? Justify your answer. (d) Suppose the test in part (c) indicates that the order in which the shows were listed does make a difference. Is the pooled value 185 + 68 = 0.527 a reasonable estimate for the proportion of students at the university 324 + 156 who would respond S ? If so, justify your answer. If not, what would be a more reasonable estimate? Explain why. END OF EXAMINATION Copyright © 2002 by College Entrance Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. 10 GO ON TO THE NEXT PAGE. 2002 AP® STATISTICS FREE-RESPONSE QUESTIONS Probability Table entry for z is the probability lying below z. z Table A z – 3.4 – 3.3 – 3.2 – 3.1 – 3.0 – 2.9 – 2.8 – 2.7 – 2.6 – 2.5 – 2.4 ...
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