An article estimates, with 90% confidence, that the proportion of elementary school teachers who are female is 82%. The article also states the maximum error of their estimate is 3%. Determine the resulting 90% confidence interval for the proportion of elementary school teachers who are female.

Question

Mathematics

Nicholas Steele

9 January, 00:46

An article estimates, with 90% confidence, that the proportion of elementary school teachers who are female is 82%. The article also states the maximum error of their estimate is 3%. Determine the resulting 90% confidence interval for the proportion of elementary school teachers who are female.

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Answers (1)

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Lee Shepard · Answer 1

Answer: (80%, 85%)

Step-by-step explanation:

We know that, confidence interval for population proportion is given by : -

(p-E, p+E)

, where p = sample proportion, E = Margin of error.

Given : Proportion of elementary school teachers who are female = 82%.

The article also states the maximum error of their estimate = 3%.

Then, the 90% confidence interval for the proportion of elementary school teachers who are female will be:

(82%-2%, 82%+3%)

= (80%, 85%)

Hence, the resulting 90% confidence interval for the proportion of elementary school teachers who are female = (80%, 85%)