A health fitness research group wishes to estimate the mean amount of time (in hours) that members of a fitness center spend each week exerc

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

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Thiên Hương 4 years 2021-08-15T23:29:20+00:00 1 Answers 46 views 0

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  1. mocmien2
    0
    2021-08-15T23:30:48+00:00
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    Answer:

    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

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