(10 marks) Uber often makes recommendations to their drivers about how to maintain their cars. Their recommendations come from studies conducted by the company. One such study considered comparing the gas mileage for two types of tire: radial or steel-belted tires. For the study, there were 20 cars available. Ten of the cars were given radial tires and the other ten cars were given steel-belted tires. Each car was driven for 5,000 miles and the gas mileage, in miles per gallon (mpg), was recoded. The results are summarized below. Steel belted tires Sample mean 34.77 mpg 30.00 mpg Sample standard deviation 2.8 mpg 3.1 mpg a. The researcher who conducted the study wished to know if these data provided evidence that the mean gas mileage for radial tires was larger than the mean gas mileage for steel belted tires (bigger gas mileage is better). What are the appropriate hypotheses for assessing the evidence of this study? b. Compute the pooled estimate, 53,, of the common population standard deviation. c. Report the value of the test statistic for testing the hypotheses in part a. d. Report the p-value for testing the hypotheses in part a (use bounds if an exact value is not available). e. Based on the p-value above, what do you conclude about the hypotheses for this study (use 3:005)