466 CHAPTERS 6–8 CUMULATIVE REVIEW CHAPTER 8 Hypothesis Testing with Two Samples 1. In a survey of 4860 U.S. adults, 77% said they would date or have already dated someone whose religion was different from theirs. (Source: Pew Research Center) (a) Construct a 95% confidence interval for the proportion of U.S. adults who say they would date or have already dated someone whose religion was different from theirs. (b) A researcher claims that more than 75% of U.S. adults say they would date or have already dated someone whose religion was different from theirs. At a = 0.05, can you support the researcher’s claim? Interpret the decision in the context of the original claim. 2. Gas Mileage The table shows the gas mileages (in miles per gallon) of eight cars with and without using a fuel additive. At a = 0.10, is there enough evidence to conclude that the additive improved gas mileage? Assume the populations are normally distributed. Car 1 2 3 4 5 6 7 8 Gas mileage (without fuel additive) 23.1 25.4 21.9 24.3 19.9 21.2 25.9 24.8 Gas mileage (with fuel additive) 23.6 27.7 23.6 26.8 22.1 22.4 26.3 26.6 In Exercises 3–6, construct the indicated confidence interval for the population mean m. Which distribution did you use to create the confidence interval? 3. c = 0.95, x = 26.97, s = 3.4, n = 42 4. c = 0.95, x = 3.46, s = 1.63, n = 16 5. c = 0.99, x = 12.1, s = 2.64, n = 26 6. c = 0.90, x = 8.21, s = 0.62, n = 8 In Exercises 7–10, the statement represents a claim. Write its complement and state which is H0 and which is Ha. 7. m 6 33 8. p Ú 0.19 9. s = 0.63 10. m ≠ 2.28 11. A pediatrician claims that the mean birth weight of a single-birth baby is greater than the mean birth weight of a baby that has a twin. The mean birth weight of a random sample of 85 single-birth babies is 3086 grams. Assume the population standard deviation is 563 grams. The mean birth weight of a random sample of 68 babies that have a twin is 2263 grams. Assume the population standard deviation is 624 grams. At a = 0.10, can you support the pediatrician’s claim? Interpret the decision in the context of the original claim.
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