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 2.9 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

We have given that to estimate the mean height of male students on your campus, you will measure an SRS of students.

standard deviation = 2.9 inches

Error (E) = 0.5

By using Emperical rule 99.7% of the data values lie within 3 standard deviation of the mean.

that is µ + 3 and µ - 3

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

That is we have to find here n(sample size)

n = [ (Zc * ) / E ]²  

where Zc is the critical value for the standard normal distribution.

c is the confidence level

Here we are not given c so we use it as 95% os 0.95.

At 95% Zc = 1.96

n = [ (1.96 * 2.9) / 0.5 ] ²

   = 11.368^2

n = 129.2314 or 130