Question

PLEASE HELP AND SHOW WORK OR DO ON CALC AND SHOW HOW TO DO IT.

A political candidate has asked you to conduct a poll to determine what percentage of people support her. If the candidate only wants a 5% margin of error at a 95% confidence level, what size of sample is needed? Give your answer in whole people. 384

Answer 1

Solution:

To find the sample size in case of unknown previous proportion, we use the below formula:

$\dpi{100} \large n=0.5(1-0.5)\left ( \frac{z_{\frac{\alpha}{2}}}{E} \right )^2$

Where:

$\dpi{100} \large z_{\frac{0.05}{2}}=1.96$ is the critical value at 0.05 significance level.

$\dpi{100} \large E=0.05$ is the margin of error.

$\dpi{100} \large \therefore n = 0.5(1-0.5)\left ( \frac{1.96}{0.05} \right )^2$

  $\dpi{100} \large = 0.25 \times 1536.64$

  $\dpi{100} \large = 384.16\approx 385$

The sample size is always rounded to the next integer.

Therefore, the required sample size is 385.