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Instructor’s Solutions Manual - Chapter 7 Chapter 7 Solutions Develop Your Skills 7.1 1. a. H 0 : p = 0.05 H 1 : p < 0.05 b. A Type I error arises when we mistakenly reject the null hypothesis when it is in fact true. This would correspond to accepting a shipment of keyboards when 5% or more of them were defective. A Type II error arises when we mistakenly fail to reject the null hypothesis when it is in fact false. This would correspond to refus ing to accept a shipment of keyboards that actually had fewer than 5% defective. c. From the manufacturer’ s point of vi ew, Type I er ror i s probably more important, because it would lead to using more faulty keyboards than desired. This would likely lead to customer complaints, and might hurt the company’s quality reputation. d. From the supplier’s point of view, the Type II error would be more frus trating, because a shipment that should have been accepted was returned. 2. a. H 0 : = 15 minutes H 1 : < 15 minutes b. A Type I error arises when we mistakenly reject the null hypothesis when it is in fact true. This would correspond to concluding that the new pain reliever provided quicker pain relief than the old formula, when in fact it didn’t. A Type II error arises when we mistakenly fail to reject the null hypothesis when it is in fact false. This would correspond to concluding that the new pain reliever did not provide quicker pain relief than the old formula, when in fact it did. c. If the company reported that it rejected the null hypothesis at a 10% signif icance level, I would not be inclined to switch to the new drug (although I would like to know the p-value to make my final decision). Such a high level of significance makes it easy to reject the null, and so there is a higher chance that it is in fact true. d. A p-value of 1% tells me the sample r esult would have occurred with a probability of only 1%, if the null hypothesis were true. This is very unlikely, yet it occurred. With such a resul t, there is strong evidence that the new pain reliever provides quicker relief than the old formula. 3. a. H 0 : = 142 ml H 1 : ≠ 142 ml This should be a two-tail ed test. Both underfilled and overfilled cans of peaches present problems. b. A Type I error arises when we mistakenly reject the null hypothesis when it is in fact true. This would corr espond to concluding the wrong amount of peaches was going into the cans, and making some adjustments, when in fact everything was fine, and no adjustments were necessary. Copyright © 2011 Pearson Canada Inc. 129
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