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

Question

To estimate the mean height mu of mole students on your campus, you will measure on SRS of students. You know from government data that the standard deviation of the heights of young men is about 2.5 inches. You want your sample mean x^- to estimate mu with on error of no more than one-half inch in either direction. What standard deviation (plusminus 0.0001) must x^- have so that 99.7% of an samples given on x^- within one-half inch of mu? (Use the 66-95-99.7 rule) How large an SRS do you need to reduce the standard deviation of x^- to the value you found in the previous part?

Explanation / Answer

a. Here Confidence level given is 99.7%

i.e. 100(1-alpha)%=99.7%

Solving this we will get alpha=99.7/100-1=0.003

Let B = error bound of our sample mean-x-bar no more than one-half inch in either direction from the population mean- .
i.e., z(alpha/2)* x-bar = 0.5
z(0.003/2)* x-bar = 0.5
z0.0015*x-bar = 0.5
2.97*x-bar = 0.5
x-bar = 0.5/2.97
x-bar = 0.1684

Hence xbar must have standard deviation to be 0.1684

b. sd calculated in a is actually standard error of xbar

Now we know SE=sd/sqrt(n)

Using this formula we can get n=(sd/SE)^2=(2.5/0.1684)^2=220.5=221

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