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What is the 99% confidence interval and why ? The manufacturer of the ColorSmart-5000 television set claims 95 percent of its sets last at least

What is the 99% confidence interval and why ?

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The manufacturer of the ColorSmart-5000 television set claims 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 366 consumers who have owned a ColorSmart-5000 television set for five years. Of these 366 consumers, 309 say their ColorSmart-5000 television sets did not need a repair, whereas 57 say their ColorSmart-5000 television sets did need at least one repair. (a) Find a 99 percent confidence interval for the proportion of all ColorSmart-5000 television sets that have lasted at least five years without needing a single repair. (Round your answers to 3 decimal places.) The 99 percent confidence interval is [ (b) Does this confidence interval provide strong evidence that the percentage of all ColorSmart-5000 television sets that last at least five years without a single repair is less than the 95 percent claimed by the manufacturer? Yes , the interval is below .95

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