478 CHAPTER 9 Inferences from Two Samples 9. Audiometry Listed below are results from subjects tested for hearing in the right ear and left ear (based on data from the National Center for Health Statistics). Values are in decibels Hearing Level (db HL) which represent the quietest sound level subjects can hear at a specific frequency. a. Use a 0.05 significance level to test the claim that the population of such differences has a mean equal to 0. b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? Right Ear 510 554010451530 520 5 Left Ear 51015525 5351015102510 10. Vision Test Listed below are results from subjects tested for visual acuity in the right eye and left eye (based on data from the National Center for Health Statistics). Lower values represent better vision. a. Use a 0.05 significance level to test the claim that the population of such differences has a mean equal to 0. b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? Right Eye 30 25 20 20 25 50 20 20 25 25 Left Eye 20 25 25 20 25 40 20 20 20 30 11. Oscars Listed below are ages of actresses and actors when they won Academy Awards for their performances (from Data Set 21 “Oscar Winner Age” in Appendix B). Each pair of ages is from the same year. a. Use a 0.05 significance level to test the claim that Oscar-winning actresses tend to be younger than Oscar-winning actors. b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? Actress (years) 28 28 31 29 35 26 26 41 30 34 Actor (years) 62 37 36 38 29 34 51 39 37 42 12. Heights of Presidents A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are heights (cm) of presidents along with the heights of their main opponents (from Data Set 22 “Presidents” in Appendix B). a. Use the sample data with a 0.05 significance level to test the claim that for the population of heights of presidents and their main opponents, the differences have a mean greater than 0 cm. b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)? Height (cm) of President 185 178 175 183 193 173 Height (cm) of Main Opponent 171 180 173 175 188 178 13. Heights of Mothers and Daughters Listed below are heights (in.) of mothers and their first daughters. The data are from a journal kept by Francis Galton. (See Data Set 10 “Family Heights” in Appendix B.) Use a 0.05 significance level to test the claim that there is no difference in heights between mothers and their first daughters. Height of Mother 68.0 60.0 61.0 63.5 69.0 64.0 69.0 64.0 63.5 66.0 Height of Daughter 68.5 60.0 63.5 67.5 68.0 65.5 69.0 68.0 64.5 63.0
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