Suppose a large telephone manufacturer has a problem with excessive customer complaints and consequent returns of the phones for repair or replacement. The manufacturer wants to estimate the magnitude of the problem in order to design a quality control program. How many telephones should be sampled and checked in order to estimate the proportion defective to within 9 percentage points with 89% confidence

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Answer:80 telephones should be sampled

Step-by-step explanation:In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following

confidence interval of proportions.In whichz is the z-score that has a p-value of .

The margin of error is of:89% confidence levelSo , z is the value of Z that has a p-value of , so .

How many telephones should be sampled and checked in order to estimate the proportion defective to within 9 percentage points with 89% confidence?n telephones should be sampled, an n is found when M = 0.09. We have no estimate for the proportion, thus we use

Rounding up(as 79 gives a margin of error slightly above the desired value).

80 telephones should be sampled