Question: The manufacturer of the ColorSmart-5000 television set claims that 95 percent of its sets last at least five years without needing a single repair. In order to test this claim, a consumer group randomly selects 400 consumers who have owned a ColorSmart-5000 television set for five years. Of these 400 consumers, 316 say that their ColorSmart-5000 television sets did not need repair, while 84 say that their ColorSmart-5000 television sets did need at least one repair.

 a.: Letting p be the proportion of ColorSmart-5000 television sets that last five years without a single repair, set up the null and alternative hypotheses that the consumer group should use to attempt to show that the manufacturer’s claim is false.

 b.: Use critical values and the previously given sample information to test the hypotheses you set up in part α by setting α equal to .10, .05, .01, and .001. How much evidence is there that the manufacturer’s claim is false?

 c.: Do you think the results of the consumer group’s survey have practical importance? Explain your opinion.

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