Suppose scores on a standard ized mathematics test taken by students from large and small high schools are normal with unkown means mux and muy respectively and known variance sigmax^2 = 56 and sigmay^2 = 47 respectively. A random sample of size n = 9 from large high school yielded a mean of xbar = 81.31 . A random sample of size m = 15 from high schools yielded a mean of ybar = 78.48.

a) What is the variance of the random variable xbar which is the mean of n=9 observations from large high schools?

b) What is the standard deviation of the random variable xbar which is the mean of n=9 from large high schools?

c) What is the variance of the random varible of ybar which is the mean of n=15 observations from small high schools?

d) What is the standard deviation of the random variable ybar which is mean of n=15 observations from small high schools?

e) What is the variance of the random variable xbar - ybar?

f) If we wish to create a 96% confidence interval for mux - muy then what is the z critical value used?

g) Why do we use z instead of t in this situation?

h) Create a 96% confidence interval for mux - muy.