Question

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 32 mpg with a standard deviation of 7 mpg. Thirty-one non-hybrid sedans get a mean of 21 mpg with a standard deviation of four 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.)

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

X_hybrid − X_non−hybrid ~ _______ (___________ , ____________)

2) 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.)   

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

4) Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value.

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

Answer 1

Since p value is less than 0.05 we reject null hypothesis. We conclude there is significant evidence to support the claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones.