Question

Estimate the average body mass of male freshman on campus. Assume that no prior information exists with which to estimate population variance σ2 but we know that the mass of most male freshmen is within a range of about 100 pounds and there are N 1000 students. How rnany samples are needed to estimate μ with a bound on the error of estimation 3 pounds using simple random sampling?
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We know that range is equal to difference of maximum value and minimum value

Using range rule of thumb for standard deviation = (range)/4

we have range = 100, so standard deviation = 100/4 = 25

Margin of error = 3

We have to find the sample size n for 95% confidence level

z score for 95% confidence level is 1.96 (using z distribution table)

Using the formula for n

we can write n = ((z*sigma)/ME)^2

setting the given values, we get

n ((1.9625)/3) (49/3)2 16.332 266.78

rounding it off to next whole number, we get

sample size n = 267

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