A sample of 50 scores on the admission test for a school of engineering is drawn at random from the scores of the persons who applied to the school in 2010. If the sample mean and the standard deviation are ¯X=546 and and s = 85,
a. Find a (approximate) 95% (two sided) confidence interval for µ, the true mean.
b. If instead the sample consisted of only 15 scores RAther than 50 and it is assumed that the scores are approximately normally distributed, find a 95% (two sided) confidence interval for µ, the true mean.
c. Using the assumptions in part b, find a 90% (two sided) confidence interval for s2.