Problem 2 {20 Points: 4, 12, 4] In a test involving highway cruising at T0 miles per hour, nine new cars of a certain make were randomly selected from the production line, and each was driven 1000 miles without an oil additive and 1000 miles with an oil additive. The order of the mo runs was independently randomized for each car. Let X1 and X2 denote the miles per gallon for a car with and without the oil additive, respectively. Data on the observed miles per gallon and their differences 0 2 X1 - X2 are summarized below. = \"PG with MPH wilhullt Adultlva [11} Addlva m Dllfaranee {KB I 11-\" 1 32.02 30.1 S 1 .39 2 25.1 9 21 .42 4.77 3 23.03 21136 0.95 4 263'? 25.94 0.82 5 27.11 29.129 -1 .39 6 33.1? 3223 1 .49 7 23.19 27'.\" 1 .03 8 31.84 30.35 1 .43 9 28.64 25.59 3.06 For these data, the sample average of the n = 9 differences is 1.55 and the sample standard deviation is 1.53. a] Is this study observational or experimental? Explain {briefly} b] Test the research hypothesis that the mean difference, Hg, is greater than zero [i.e., that the additive leads to an increase in miles per gallon on average}. Give the null and alternative hypotheses, compute the test statistic, and identify the rejection region. What do you conclude? Use 0'. = 0.05