SECTION 8.1 Testing the Difference Between Means (Independent Samples, s1 and s2 Known) 425 12. Claim: m1 7 m2; a = 0.10 Population statistics: s1 = 40 and s2 = 15 Sample statistics: x1 = 500, n1 = 100 and x2 = 495, n2 = 75 13. Claim: m1 6 m2; a = 0.05 Population statistics: s1 = 75 and s2 = 105 Sample statistics: x1 = 2435, n1 = 35 and x2 = 2432, n2 = 90 14. Claim: m1 … m2; a = 0.03 Population statistics: s1 = 136 and s2 = 215 Sample statistics: x1 = 5004, n1 = 144 and x2 = 4895, n2 = 156 Using and Interpreting Concepts Testing the Difference Between Two Means In Exercises 15–24, (a) identify the claim and state H0 and Ha, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic z, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. 15. Braking Distances To compare the dry braking distances from 60 to 0 miles per hour for two makes of automobiles, a safety engineer conducts braking tests for 16 compact SUVs and 11 midsize SUVs. The mean braking distance for the compact SUVs is 131.8 feet. Assume the population standard deviation is 5.5 feet. The mean braking distance for the midsize SUVs is 132.8 feet. Assume the population standard deviation is 6.7 feet. At a = 0.10, can the engineer support the claim that the mean braking distances are different for the two categories of SUVs? (Adapted from Consumer Reports) 16. Bed-in-a-Box To compare customer satisfaction with mattresses that are delivered compressed in a box and traditional mattresses, a researcher randomly selects 30 ratings of mattresses in boxes and 30 ratings of traditional mattresses. The mean rating of mattresses in boxes is 68.7 out of 100. Assume the population standard deviation is 6.6. The mean rating of traditional mattresses is 70.9 out of 100. Assume the population standard deviation is 5.6. At a = 0.01, can the researcher support the claim that the mean rating of traditional mattresses is greater than the mean rating of mattresses in a box? (Adapted from Consumer Reports) 17. Wind Energy An energy company wants to choose between two regions in a state to install energy-producing wind turbines. A researcher claims that the wind speed in Region A is less than the wind speed in Region B. To test the regions, the average wind speed is calculated for 60 days in each region. The mean wind speed in Region A is 14.0 miles per hour. Assume the population standard deviation is 2.9 miles per hour. The mean wind speed in Region B is 15.1 miles per hour. Assume the population standard deviation is 3.3 miles per hour. At a = 0.05, can the company support the researcher’s claim? 18. Repair Costs: Washing Machines You want to buy a washing machine, and a salesperson tells you that the mean repair costs for Model A and Model B are equal. You research the repair costs. The mean repair cost of 24 Model A washing machines is $208. Assume the population standard deviation is $18. The mean repair cost of 26 Model B washing machines is $221. Assume the population standard deviation is $22. At a = 0.01, can you reject the salesperson’s claim?
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