Estimate of Proportion An airline is interested in determining

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r1fa8dy5

Answered question

2022-04-03

Estimate of Proportion
An airline is interested in determining the proportion of its customers who are flying for reasons of business. If they want to be 90 percent certain that their estimate will be correct to within two percent, how large a random sample should they select?
This involves using the Z-distribution to find the 90% confidence interval of the actual value of the proportion. But for this to be done, there needs to be an estimate of the proportion, which is not given. How do we find this out?ie
(p)(1p)za2n=0.0004. How do we find the value of p?

Answer & Explanation

Karsyn Wu

Karsyn Wu

Beginner2022-04-04Added 17 answers

Take the most "pessimistic" estimate of p(1p), that is, the largest possible variance. Note that the maximum value of p(1p) is 14, attained at p=12.
The standard deviation of the sample mean is therefore 12n. So we use 12n.
Remarks: 1. There may be a mistake, or at least a typo, in your equation. Probably zα22 is intended.
2. After the experiment has been performed, if p^ turns out to be not far from 0 or not far from 1, one may conclude that one has obtained a better estimate than the one planned for. However, p(1p) stays remarkably close to 14 for p not too far from 12.

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