Question

Read and analyze the given problem. Provide a complete solution, Table, and a graph corresponds to the answer.

Based from the result of a survey conducted by a group of researchers, the proportion of females holding executive positions in the government agencies in a certain populated city is normally distributed. In a random sample of 300 female employees in the government agencies, 75 female hold executive positions.

Compute the proportion estimate of the population

Compute for the margin of error of the proportion at 90% CL.

Find 90% and 95% CI for all the female employees in the government agencies holding executive positions.

Interpret the result.

Answer 1

We have given $n = 300$

1.) Proportion estimate of the population $= \dfrac{75}{300} = p = 0.25$

2.) Margin error $= z\times \sqrt{\dfrac{p(1-p)}{n}}$

$z = 1.645$

Margin error $= 1.645 \times \sqrt{\dfrac{0.75\times 0.25}{300}} = 0.041$

3.) 90% confidence interval

$CI = p \pm z\sqrt{\dfrac{p(1-p)}{n}}$

$CI = 0.25 \pm 1.645\times \sqrt{\dfrac{0.25\times 0.75}{300}}$

$CI = 0.25 \pm 0.041$

95% confidence interval

$CI = p \pm z\sqrt{\dfrac{p(1-p)}{n}}$

$CI = 0.25 \pm 1.96\times \sqrt{\dfrac{0.25\times 0.75}{300}}$

$CI = 0.25 \pm 0.049$