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 356 consumers who have owned a ColorSmart-5000 television set for five years. Of these 356 consumers, 322 say their ColorSmart-5000 television sets did not need a repair, whereas 34 say their ColorSmart-5000 television sets did need at least one repair.

rev: 11_17_2014_QC_59045

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 356 consumers who have owned a ColorSmart-5000 television set for five years. Of these 356 consumers, 322 say their ColorSmart-5000 television sets did not need a repair, whereas 34 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

We know that the margin of error is given as

Z0.01/2*(p*(1-p)/n)1/2 = 0.03 where p =322/356 = 0.90

Z0.005*(0.90*(1-0.9)/n)1/2 = 0.03 => 2.576*(0.0.09/n)1/2 = 0.03

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