To estimate the mean height mu of male students on your campus, you will measure

Question

To estimate the mean height mu of male students on your campus, you will measure an SRS of students. You know from government data that heights of young men are approximately Normal with standard deviation about 2.8 inches. You want your sample mean x bar to estimate mu with an error of no more than one-half inch in either direction. (a) What standard deviation must x bar have so that 68% of all samples give an x bar within one-half inch of mu? (Use the 68-95-99.7 rule.) (b) How large an SRS do you need to reduce the standard deviation of x bar to the value you found in part(a)? (a) (b)

Explanation / Answer

a) for 68% values lies with in one std deviation from mean. therefore sample mean should have std deviation equal to margin of error.

therefore std deviation of mean =1/2 =0.5 inch

b) std deviation of mean =std deviation of population/(n)1/2

hence sample size =(2.8/0.5)2 =31.36~32

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