Question

Determine the average time (in seconds) required to perform some type of physical labor: What is the required sample size to be 99% certain that the sample mean will be within 15 seconds of the true average, if the standard deviation of the time is σ = 30 seconds?

Answer 1

Solution :

Given that,

Population standard deviation = $\sigma$ = 30

Margin of error = E = 15

Z_$\alpha$/2 = 2.576

sample size = n = [Z_$\alpha$/2* $\sigma$ / E] ²

n = [2.576 * 30 / 15]²

n = 27

Sample size = n = 27