The manufacture of the ColorSmart-5000 television set would like to claim 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 their colorsmart-5000 television sets did not need a repair, whereas 84 say their colorsmart-5000 television sets did need atleast one repair
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a. Find a 99 percent confident interval for the proportion of all colorsmart-5000 television sets that have lasted at least five years without needing a single repair
b. Does this confidence interval provide strong evidence that the percentage of colorsmart-5000 television sets that last atleast five years without a single repair is less than the 95 percent claimed by the manufacturer? Yes or no? Expain.
c. Determine the sample size needed in order to be 99 percent confident that p-hat, the sample proportion of colorsmart-5000 television sets that last atleast five years without a single repair, is within .03 of p, the true proportion of sets that last atleast five years without a single repair