Question
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
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.
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