Question

Emma Watson, who is employed by a major investment firm in LA would like to estimate the percentage of new clients who will make a certain type of investment. If she wants a sampling error no greater than +/- 2.5% and a confidence level of 95%, how many clients should she sample?

Please provide step by step instructions and details.

Answer 1

Given that, margin of error ( E ) = 2.5% = 0.025

confidence level = 95%

A 95% confidence level has significance level $(\alpha)$ = 0.05 and critical value is, $Z_{\alpha/2} = 1.96$

Since, we don't have the estimate of the proportion we assume it to be 0.5. That is, p = 0.5

We want to find, the sample size ( n ),

$n = p * (1-p) * (\frac {Z_{\alpha/2} }{E})^2 = 0.5 *(1-0.5)*(\frac { 1.96}{0.025})^2 = 1536.64$

$\inline n \approx 1537$

Therefore, required sample size is 1537