Question: In May 2008, CNN reported that Sports Utility Vehicles (SUVs) are plunging toward the "endangered" list. Due to soaring oil prices and environmental concerns, consumers are replacing gas-guzzling vehicles with fuel-efficient smaller cars. As a result, there has been a big drop in the demand for new as well as used SUVs. A sales manager of a used car dealership believes that it takes 30 days longer to sell an SUV as compared to a small car. In the last two months, he sold 18 SUVs that took an average of 95 days to sell with a standard deviation of 32 days. He also sold 38 small cars with an average of 48 days to sell and a standard deviation of 24 days.
a. Construct the null and the alternative hypotheses to contradict the manager's claim.
b. Compute the value of the test statistic under the assumption that the variability of selling time for the SUVs and the small cars is the same.
c. Implement the test at α = 0.10 and interpret your results.