Hypothesis Testing for #1 - 2 Exercise 1 Data on household vehicle miles of travel (VMT) are compiled annually by the Federal Highway Administration. A researcher is interested in whether there is a difference in last year's mean VMT for Midwestern and southern households (M and s). Independent random samples of 15 Midwestern households and 14 southern households provided the following data on last year's VMT, in thousands of miles: Midwest: 16.2, 12.9, 17.3, 14.6, 18.6, 10.8, 11.2, 16.6, 16.6, 24.4, 20.3, 20.9, 9.6, 15.1, 18.3 South: 22.2, 19.2, 9.3, 24.6, 20.2, 15.8, 18.0, 12.2, 20.1, 16.0, 17.5, 18.2, 22.8, 11.5 a. Graph the data as you see fit. Why did you choose the graph(s) you did and what does it (do they) tell you? Also calculate summary statistics relevant to the research question. b. Perform a 10% level two sample t test for means assuming equal variance to address the researcher's question. Justify why the assumptions of the test are reasonably met or describe what assumptions we are assuming are met. As part of this test, specify your hypotheses, calculate your test statistic, p value and make a conclusion in the context of the question (Highlight these values in your solutions). Show all steps of the computation and then check your computations using t.test. c. Construct a 90% confidence interval for the true difference in means assuming equal population variances (by hand and then again in R). Label the point estimate for - s and the components of the confidence interval's margin of error. Discuss the relationship between your findings in 1b and 1c.