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

the smallest sample size is 163

Step-by-step 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

step-by-step explanation:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.