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.
A) 323
B) 12
C) 457
D) 14
E) 100

Question

Quizplus · Accepted Answer

The formula for sample size calculation in estimating population proportions is: 
n = (Z^2 * p * q) / E^2 
where 
n = sample size 
Z = Z-value for desired level of confidence (in this case, 2.33 for 98% confidence) 
p = estimated proportion of non-business e-mails (0.30) 
q = 1 - p 
E = maximum allowable error (0.05)

Plugging in the values: 
n = (2.33^2 * 0.30 * 0.70) / 0.05^2 = 457.47

Rounding up to the nearest whole number, Elwin should sample 457 e-mail messages to achieve the desired level of precision and confidence.