Question

A health fitness research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend each week exercising at the center. They want to estimate the mean within a margin of error of 0.4 hours with a 95% level of confidence. Previous data suggest that the population standard deviation (sigma) is 2.6 hours. What is the smallest sample size that meets these criteria

Answer 1

the smallest sample size is 163

Explanation:

The computation of the smallest sample size that meets these criteria is shown below:

n = (Z a/2 × Standard deviation ÷ Margin of error ) ^2

Zα/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )

Standard Deviation ( S.D) = 2.6

Margin of error i.e. ME =0.4

n = ( 1.96 × 2.6 ÷ 0.4) ^2

= 163

Hence, the smallest sample size is 163