The sample size needed to estimate a population mean to within 2 units with a 95% confidence when the population standard deviation equals 8 is:
A)9.
B)61.
C)62.
D)8.

Question

Quizplus · Accepted Answer

The formula for calculating the sample size needed to estimate a population mean with a 95% confidence interval when the population standard deviation is known is:
n = (z*(σ/√n))/E
where:
z = the z-score for the desired confidence level (1.96 for 95%)
σ = the population standard deviation (8)
E = the desired margin of error (2)

Substituting the given values into the formula:
n = (1.96*(8/2))^2 = 61.44

Since sample sizes must be whole numbers, the next highest integer must be chosen, which is 62. Therefore, the answer is C.

The Sample Size Needed to Estimate a Population Mean to Within