A car company made a change to their fuel injection system that may improve gas mileage. To determine if this was the case, they selected 24 new cars at random from several days of production. The cars were randomly assigned to two groups of 12 cars each. One of these groups was fitted with the experimental fuel injection system, and the second was fitted with the current fuel injection system.
All the cars were driven around the same predetermined route, whose distance was known. By dividing the quantity of gas used by this driving distance, the automobile company was able to determine the gas mileage of each car. In summarizing the results, they found that the cars with the experimental fuel injection system had an average gas mileage of 33.4 mi/gal with a standard deviation of 1.3 mi/gal. Cars fitted with the current fuel injection system had an average gas mileage of 28.6 mi/gal with a standard deviation of 2.0 mi/gal.
- How would you construct a test of hypothesis to determine whether or not cars with the experimental fuel injection system provide better gas mileage than cars with the current fuel injection system. (State the null and alternative hypotheses, give the test statistic that you would use, and state the most accurate distribution of this test statistic. Note, this is a one-sided test of hypothesis.) Because the improved system may result in the more consistent use of gas, don't assume that the standard deviations of the two populations are equal.
- Can you conclude at a significance level of 5% that the gas mileage of the experimental fuel injection system is better than that of the current fuel injection system?
- Describe how you would conduct this test of hypothesis as a single-blind study. What are the advantages of designing the study in this fashion?