For all problems, your answers should be as specific to the problem as possible and you should not use general notation. As an example, you should make reference to mu (Psychology Majors) and not simply refer to them as mu(1). To answer the why questions for the statistical conclusions, simply use the most important rule for hypothesis tests and fill in the specific values for the problem. If the p-value from the output needs to be adjusted, show the adjustment in your work. 1. A researcher has a theory that Michigan graduates who were Psychology majors are even more awesome than Michigan graduates who were Political Science majors. He tests a set of Michigan Psychology majors and Michigan Political Science majors using his awesome-o-meter, which produces an awesomeness score between 1 and 100. Fill in the required information based on the description of this problem and the sample sizes listed in the table below. n=40 for both majors n=10 for both majors What is the specific name of the statistical test to evaluate the researcher's question according to the lecture slides and book (not the test used in SPSS) What are Ho and Ha for the test? Assume that for the small n that we do not know anything about the population distributions for either group. The output for the smaller n of the two columns above is shown above. What is the statistical conclusion (reject... vs. ....) for an alpha of 10% and very briefly why? All else the same as above, what is the statistical conclusion if alpha=5% and very briefly why? What is the p-value for the research question described using either of the p-values in the output. 2. Even the most awesome people could use a little training to help improve their awesomeness. A group of Michigan graduates has their awesomeness measured using awesome-o-meter (mentioned previously), they are then given a week of training on how to improve their awesomeness. Their awesomeness is then measured again at the end of the week. Their pre-training scores are subtracted from their post training scores. Fill in the required information based on the description of this problem and the sample sizes listed in the table below. n=55 n=12 What is the specific name of the statistical test to evaluate the research question? What are Ho and Ha for the test? Assume that for the small n that we do not know anything about the population distribution. The output for the smaller n of the two columns above is shown above. What is the statistical conclusion (reject... vs. ....) for an alpha of 10% and very briefly why? All else the same as above, what is the statistical conclusion if alpha=5% and very briefly why? 3. An evil Ohio State Graduate (although that is redundant) wants to test five different poisons in hopes that some of them will reduce the awesomeness of Michigan graduates. He slips the poison into the diet of a set of five groups of Michigan graduates and then secretly has their awesomeness measured using the awesome-o-meter. Due to his lack of imagination he labels the poisons A, B, C, D, E. n=41 for all groups n=11 for all groups What is the specific name of the statistical test to evaluate the researcher's question? What are Ho and Ha for the test? Assume that for the small n that we do not know anything about the population distributions for either group. The output for the smaller n of the two columns above is shown above. What is the statistical conclusion (reject... vs. ....) for an alpha of 10% and very briefly why? All else the same as above, what is the statistical conclusion if alpha=5% and very briefly why? Non Parametric: 1. 2. 3. 4. Wilcoxon Signed Rank Test Wilcoxon Signed Rank Test on differences Wilcoxon Rank Sum Test Kruskall-Wallis Test 1. 2. 3. 4. Other: T-test for single mean T-test for difference of matched pairs T-test for two means ANOVA