Consider an ANOVA setup with k groups, as in class. In some cases, you might just be interested in two of the groups, i and j. Of course, you could extract these two columns (ignoring the other groups) and run a two-sample t-test (with unknown and equal variances), but here's another idea Since the variance is supposed to be equal in all the groups of the ANOVA, we could use all the data (not just the data in groups i and j) when approximative o for our test statistic. Define SSE = (which uses all the data and does not depend on i or j) and show its expectation n - k Y.i - Y.j is o2. Finally, define taj = and explain how t can be used to conduct a test for S + ni nj the equality of the means of the data in columns i and j. (In particular, you should find the distribution of the statistic tij.)