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Suppose a large telephone manufacturer has a problem with excessive customer complaints and consequent returns of the phones for repair or r
Question
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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Mathematics
3 years
2021-08-10T09:21:56+00:00
2021-08-10T09:21:56+00:00 1 Answers
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Answers ( )
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 which
z is the z-score that has a p-value of
.
The margin of error is of:
89% confidence level
So
, 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![Rendered by QuickLaTeX.com \pi = 0.5](https://documen.tv/wp-content/ql-cache/quicklatex.com-680f4747f98eda845373e5c1ea163b8e_l3.png)
Rounding up(as 79 gives a margin of error slightly above the desired value).
80 telephones should be sampled