You want to determine the average amount spent by campers on food at a local sta

Question

You want to determine the average amount spent by campers on food at a local state campsite. You would like your estimate to be within plus or minus $25 of the true population value. You would like 95% confidence in the interval you calculate, so you will use z = 1.96 (the correct z value for 95% confidence). You go through the last few years of estimates and you discover that the historic variation in expenditures on food, as measured by standard deviation is 100. a. What sample size would you recommend so that you can achieve your confidence and precision goals? b. If you wanted to increase confidence to 99%, how much does your required sample size change? (for 99%, use z = 2.575) c. Now, reset confidence to 95%. If you wanted to double the precision (that is, get MORE precise), how much does your required sample size change?

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) = 100
ME =25
n = ( 1.96*100/25) ^2
= (196/25 ) ^2
= 61.466 ~ 62      
b.
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Z/2 at 0.01% LOS is = 2.58 ( From Standard Normal Table )
Standard Deviation ( S.D) = 100
ME =25
n = ( 2.58*100/25) ^2
= (258/25 ) ^2
= 106.502 ~ 107  

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