In a class of 50 students, the result of a particular examination is a true mean of 70 and a true variance of 12. It is desired to estimate the mean by sampling, without replacement, a subset of the scores.
a) Find the standard de.viation of the sample mean if only 10 scores are used.
b) How large should the sample size be for the standard deviation of the sample mean to be one percentage point (out of 100)?
c) How large should the sample size be for the standard deviation of the sample mean to be 1 % of the true mean?