Question

Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications. He plans to use a 98% confidence interval estimate of the proportion of e-mail messages that are non-business; he will accept a 0.05 error. Previous studies indicate that approximately 30% of employee e-mail is not business related. Elwin should sample _______ e-mail messages.

Answer 1

Answer: 456

Explanation:

Given : Significance level : $\alpha= 1-0.98=0.02$

Critical value : $z_{\alpha/2}=2.33$

Margin of error : $E=\pm0.05$

The prior proportion of employee e-mail is not business related: $p=0.30$

The formula to find the sample size is given by :-

$n=(p(1-p))(\dfrac{z_{\alpha/2}}{E})^2$

i.e. $n=(0.3(0.7))(\dfrac{(2.33)}{0.05})^2=456.0276\approx456$

Hence, Elwin should sample 456 e-mail messages.