Using principles from this chapter, inferentially compare ????1 and ????2 from N(????1, ????2) and N(????2, ????2) populations, based on independent random samples of sizes n1 and n2.

a. Put the analysis in a normal linear model context, showing a model matrix and explaining how to interpret the model parameters.

b. Find the projection matrix for the model space, and find SSR and SSE.

c. Construct a F test statistic for testing H0: ????1 = ????2 against Ha: ????1 ≠ ????2.

Using Cochran’s theorem, specify a null distribution for this statistic.

d. Relate the F test statistic in

(c) to the t statistic for this test, t = ȳ1 − ȳ2 s

√ 1 n1

+ 1 n2 where s2 is the pooled variance estimate from the two samples.