Question

13 multiple choice 4 points construct the requested confidence interval. 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 (82%, 85%) (79%, 82%) (80.5%, 83.5%) (87%, 93%) (79%, 85%)

Explanation:

Step1: Recall confidence interval formula

The confidence interval for a proportion is given by $\hat{p}-E

Step2: Substitute values

Here, $\hat{p}=82\%$ and $E = 3\%$.
Substituting into the formula:
Lower limit: $82\% - 3\%=79\%$
Upper limit: $82\%+3\% = 85\%$

Answer:

$(79\%,85\%)$