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Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 21 hybrid sedans and get a mean of 30 mpg with a standard deviation of 6 mpg. Thirty-one non-hybrid sedans get a mean of 21 mpg with a standard deviation of three mpg. Suppose that the population standard deviations are known to be six and three, respectively. Conduct a hypothesis test at the 5% level to evaluate the manufacturers claim. NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) Part (a) Part (b) Part (c) Part (d) Part (e) What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.) ---Select--- O= Part (f) What is the p-value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. O If Ho is true, then there is a chance equal to the p-value that the sample average gas mileage of non-hybrid sedans is 9 mpg more than the sample average gas mileage of hybrid sedans. O If Ho is true, then there is a chance equal to the p-value that the sample average gas mileage of non-hybrid sedans is at least 9 mpg less than the sample average gas mileage of hybrid sedans. If Ho is false, then there is a chance equal to the p-value that the sample average gas mileage of non-hybrid sedans is at least 9 mpg less than the sample average gas mileage of hybrid sedans. If Ho is false, then there is a chance equal to the p-value that the sample average gas mileage of non-hybrid sedans is 9 mpg more than the sample average gas mileage of hybrid sedans