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 theirColorSmart-5000television sets did need at least one repair.

(a)Lettingpbe 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 partaby settingequal to .10, .05, .01, and .001. How much evidence is there that the manufacturer's claim is false?