SECTION 7.2 Hypothesis Testing for the Mean (s Known) 375 Using and Interpreting Concepts Hypothesis Testing Using a P-Value In Exercises 33–38, (a) identify the claim and state H0 and Ha. (b) find the standardized test statistic z. (c) find the corresponding P@value. (d) decide whether to reject or fail to reject the null hypothesis. (e) interpret the decision in the context of the original claim. 33. MCAT Scores A random sample of 100 medical school applicants at a university has a mean total score of 505 on the MCAT. According to a report, the mean total score for the school’s applicants is more than 503. Assume the population standard deviation is 10.6. At a = 0.01, is there enough evidence to support the report’s claim? (Adapted from Association of American Medical Colleges) 34. Sprinkler Systems A manufacturer of sprinkler systems designed for fire protection claims that the average activating temperature is at least 135°F. To test this claim, you randomly select a sample of 32 systems and find the mean activation temperature to be 133°F. Assume the population standard deviation is 3.3°F. At a = 0.10, do you have enough evidence to reject the manufacturer’s claim? 35. Boston Marathon A sports statistician claims that the mean winning times for Boston Marathon women’s open division champions is at least 2.6 hours. The mean winning time of a sample of 30 randomly selected Boston Marathon women’s open division champions is 2.52 hours. Assume the population standard deviation is 0.18 hour. At a = 0.05, can you reject the claim? (Adapted from Boston Athletic Association) 36. Acceleration Times A consumer group claims that the mean acceleration time from 0 to 60 miles per hour for all 3-cylinder vehicles is 9.4 seconds. A random sample of 33 3-cylinder vehicles has a mean acceleration time from 0 to 60 miles per hour of 10.2 seconds. Assume the population standard deviation is 2.3 seconds. At a = 0.05, can you reject the claim? (Adapted from Zero to 60 Times) 37. Roller Coasters The vertical drops (in feet) of 36 randomly selected top-rated roller coasters are listed. Assume the population standard deviation is 65.1 feet. At a = 0.05, is there enough evidence to reject the claim that the mean vertical drop of top-rated roller coasters is 163 feet? (Adapted from Coasterpedia ) 100 100 131 116 98 306 180 118 103 210 215 249 115 104 72 195 135 100 161 98 89 131 98 151 98 171 154 151 161 256 98 119 125 131 80 300 38. Salaries An analyst claims that the mean annual salary for intermediate level electrical engineers in Baltimore, Maryland, is more than the national mean, $86,700. The annual salaries (in dollars) for a random sample of 21 intermediate level electrical engineers in Baltimore are listed. Assume the population is normally distributed and the population standard deviation is $13,600. At a = 0.09, is there enough evidence to support the analyst’s claim? (Adapted from Salary.com) 71,323 87,322 88,900 75,212 89,516 92,345 95,100 78,444 92,634 96,117 90,309 97,818 86,437 103,345 97,722 93,676 89,925 90,121 92,008 91,555 86,544
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