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 355 consumers who have owned a ColorSmart-5000 television set for five years. Of these 355 consumers, 302 say their ColorSmart-5000 television sets did not need a repair, whereas 53 say their ColorSmart-5000 television sets did need at least one repair.

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 355 consumers who have owned a ColorSmart-5000 television set for five years. Of these 355 consumers, 302 say their ColorSmart-5000 television sets did not need a repair, whereas 53 say their ColorSmart-5000 television sets did need at least one repair.

Determine the sample size needed in order to be 99 percent confident that , the sample proportion of ColorSmart-5000 television sets that last at least five years without a single repair, is within a margin of error of .03 of p, the population proportion of sets that last at least five years without a single repair.(Round your p answer to 5 decimal places. Round your n answer to the next whole number.)

Explanation / Answer

alpha / 2 = 0.005 Z = 2.575

p = 302 / 355 = 0.86 error = 0.03

n = 2.575^2 * 0.86 * 0.14 / 0.03^2

n = 887.03

n = 888

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