426 CHAPTER 8 Hypothesis Testing with Two Samples 19. ACT Mathematics and Science Scores The mean ACT mathematics score for 60 high school students is 20.2. Assume the population standard deviation is 5.7. The mean ACT science score for 75 high school students is 20.6. Assume the population standard deviation is 5.9. At a = 0.01, can you reject the claim that ACT mathematics and science scores are equal? (Source: ACT, Inc.) 20. ACT English and Reading Scores The mean ACT English score for 120 high school students is 19.9. Assume the population standard deviation is 7.2. The mean ACT reading score for 150 high school students is 21.2. Assume the population standard deviation is 7.1. At a = 0.10, can you support the claim that ACT reading scores are higher than ACT English scores? (Source: ACT, Inc.) 21. Home Prices A real estate agency says that the mean home sales price in Casper, Wyoming, is the same as in Cheyenne, Wyoming. The mean home sales price for 35 homes in Casper is $349,237. Assume the population standard deviation is $158,005. The mean home sales price for 41 homes in Cheyenne is $435,244. Assume the population standard deviation is $154,716. At a = 0.01, is there enough evidence to reject the agency’s claim? (Adapted from Realtor.com) 22. Home Prices In Exercise 21, an additional home in Casper sells for $132,000, and another in Cheyenne sells for $495,000. Add these data to the existing samples. At a = 0.01, do the adjusted samples lead to a different conclusion? (Adapted from Realtor.com) 23. Precipitation A climatologist claims that the precipitation in Seattle, Washington, was greater than in Birmingham, Alabama, in a recent year. The daily precipitation amounts (in inches) for 30 days in a recent year in Seattle are shown below. Assume the population standard deviation is 0.25 inch. 0.00 0.00 0.05 0.01 0.21 0.00 0.00 0.52 0.00 0.01 0.00 0.19 0.00 0.18 0.02 0.02 0.13 0.00 0.03 0.00 0.04 0.00 0.41 0.23 0.00 0.80 0.15 0.00 0.00 0.79 The daily precipitation amounts (in inches) for 30 days in a recent year in Birmingham are shown below. Assume the population standard deviation is 0.52 inch. 0.00 0.96 0.84 0.00 0.10 0.00 0.00 0.20 0.00 0.54 0.97 0.00 0.35 0.02 0.04 0.70 0.00 0.00 0.00 0.00 0.03 0.01 0.15 0.27 0.00 0.00 0.93 0.00 0.89 0.01 At a = 0.05, can you support the climatologist’s claim? (Source: NOAA) 24. Temperature A climatologist claims that the temperature in Seattle, Washington, was lower than in Birmingham, Alabama, in a recent year. The maximum daily temperatures (in degrees Fahrenheit) for 30 days in a recent year in Seattle are shown below. Assume the population standard deviation is 12.0°F. 52 45 66 49 62 74 80 75 76 65 67 75 57 50 46 49 53 57 60 70 85 56 60 44 59 65 70 73 61 61 The maximum daily temperatures (in degrees Fahrenheit) for 30 days in a recent year in Birmingham are shown below. Assume the population standard deviation is 13.2°F. 64 60 91 85 59 93 90 73 87 72 50 58 79 72 85 57 73 61 89 69 60 93 56 74 94 66 63 91 94 73 At a = 0.01, can you support the climatologist’s claim? (Source: NOAA)
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