Find a 95% confidence interval for the true population proportion.
-In a survey of 257 female employees of a large company, 21% said that they had experienced some form of sexual harassment while working for the company.
A) $20.6 \%$ to $21.4 \%$
B) $14.8 \%$ to $27.2 \%$
C) $8.5 \%$ to $33.5 \%$
D) $20.9 \%$ to $21.1 \%$

Question

Find a 95% confidence interval for the true population proportion.
-In a survey of 257 female employees of a large company, 21% said that they had experienced some form of sexual harassment while working for the company. 
A) $20.6 \%$ to $21.4 \%$
B) $14.8 \%$ to $27.2 \%$
C) $8.5 \%$ to $33.5 \%$
D) $20.9 \%$ to $21.1 \%$

Quizplus · Accepted Answer

To find a 95% confidence interval for the population proportion, we use the formula: $\hat{p} \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$, where $\hat{p} = 0.21$, $n = 257$, and $Z_{\alpha/2} = 1.96$ for a 95% confidence level. Plugging these values into the formula gives us the interval $0.148$ to $0.272$ or $14.8\%$ to $27.2\%$.

Find a 95% Confidence Interval for the True Population Proportion 20.6%20.6 \%20.6%

Find a 95% Confidence Interval for the True Population Proportion $20.6 \%$