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 of30mpgwith a standard deviation of8mpg.Thirty-one non-hybrid sedans get a mean of20mpgwith a standard deviation ofthreempg.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'st-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.)

1.State the distribution to use for the test. (Round your answers to two decimal places.)

2.What is the test statistic? (If using thezdistribution round your answer to two decimal places, and if using thetdistribution round your answer to three decimal places.)

3.What is thep-value? (Round your answer to four decimal places.)

4.Alpha (Enter an exact number as an integer, fraction, or decimal.) =