The manufacturer of the ColorSmart-5000 television set claims 95 percent of its

Question

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 403 consumers who have owned a ColorSmart-5000 television set for five years. Of these 403 consumers, 308 say their ColorSmart-5000 television sets did not need a repair whereas 95 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? (Click to select), the interval is (Click to select). 95.

Explanation / Answer

a) The statistical software output for this problem is:

One sample proportion confidence interval:
p : Proportion of successes
Method: Standard-Wald

99% confidence interval results:

So,

The 99% confidence interval is [0.710, 0.819].

b) Yes, since the interval contains the proportions which are less than 95%. 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.

Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit p 308 403 0.76426799 0.021143632 0.7098056 0.81873038

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