To estimate the mean height of male students on your campus

To estimate the mean height of male students on your campus, you will measure an SRS of students. You know from government data that the standard deviation of the heights of young men is about 3.1 inches. You want your sample mean x to estimate with an error of no more than one-half inch in either direction.

What standard deviation (±0.0001) must x have so that 99.7% of all samples give an x within one-half inch of ? (Use the 68-95-99.7 rule)

How large an SRS do you need to reduce the standard deviation of x to the value you found in the previous part?

Solution

z for a 99.7% of all samples = 2.967738.....

2.967738 = (x-bar - ) / (s.d / sqrt(n) )

or, 0.5 / ( s.d/ sqrt(n) ) = 2.967738

or, 0.5 / 2.967738 = ( s.d / sqrt(n) )

or, standard deviation x-bar should have so that 99.7% of all samples give an x-bar within 1/2 inch of = 0.1684785........

b) [ (s.d) / sqrt(n) ] = 0.1684785........

or, (3.1/ 0.1684785 ) = sqrt(n)......or, n = 338.559 or nearly equals = 339.....