A health fitness research group wishes to estimate the mean amount of time (in h
ID: 3152845 • Letter: A
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 0.5 hours with a 95% level of confidence. Previous data suggests that = 2.2 hours. What is the smallest sample size that meets these criteria?
A researcher wishes to use a 92% confidence interval to estimate the proportion of Americans who have visited an entertainment theme park near Orlando within the last five years. The researcher wishes to choose a size that will ensure a margin of error not to exceed 0.05. What is the smallest size that meets these criteria?
Explanation / Answer
a.
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.05% LOS is = 1.96 ( From Standard Normal Table )
Standard Deviation ( S.D) = 2.2
ME =0.5
n = ( 1.96*2.2/0.5) ^2
= (4.312/0.5 ) ^2
= 74.373 ~ 75
b.Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.08 is = 1.751
Sample Proportion = 0.5
ME = 0.05
n = ( 1.751 / 0.05 )^2 * 0.5*0.5
= 306.6 ~ 307
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