A sample from population 1 yields

y1 = c(0.9558698, 1.3898674, 0.4734109, -0.8553562, 1.2512193, 1.5965338, 1.2513180, 0.7604499, 1.9638653, 1.2406462)

A sample from population 2 yields

y2 = c(1.6233814, 0.4932769, 1.1456087, 2.5006349, 1.5444356, 0.3170836, 3.6545359, 1.9662585, 2.1142919)

1) We ask the question "Does data provide evidence for mu1 mu2. Write the appropriate hypotheses.

2) Assume the two populations have equal variance. If a t-test is used, at alpha = 0.05, what is the rejectionregion?

3) Compute the appropriate observed value of the t statistic. Based on your answers to parts 1-3, answer thequestion in part 1.

4, 5) Suppose we cannot assume the two populations have equal variance. Repeat parts 2 and 3.

6) Now, we ask "Is there evidence from data that sigma1 != sigma2 ?" Write the appropriate hypotheses.

7) Use the fact that, assuming sigma1=sigma2, then var1/var2 has an F distribution with df=(n1-1,n2-1), tofind the rejection region.

8) Compute the appropriate observed value of the F statistic. Based on your answers to parts 1-8, answer thequestion in part 6.