Question

An engineer believes that her newly designed engine will be a great gas saver. A large number of tests on engines of the old design yielded a mean gasoline consumption of 19.5 miles per gallon with a standard deviation of 5.2. Fifteen new engines were tested. the mean gasoline consumption is 21.6 miles per gallon. What is the appropriate analysis?

Answer 1

The hypothesis test appropriate for comparing the fuel consumption of new and old engine designs is a one-sample t-test. The test will determine if there is a statistically significant improvement in the new design's fuel efficiency compared to the established mean of the old design.

Step-by-step explanation:

The appropriate analysis for the situation described, where an engineer tests 15 new engines with a mean gasoline consumption of 21.6 miles per gallon compared to the old design with a mean of 19.5 and a standard deviation of 5.2, is to perform a hypothesis test. Specifically, we would use a one-sample t-test to determine if the new design statistically significantly exceeds the old design's mean fuel consumption.

To conduct this test, we would:

1. State the null hypothesis, which is that the new engine design does not improve fuel consumption (mean = 19.5 mpg).
2. State the alternative hypothesis, which is that the new engine design does improve fuel consumption (mean > 19.5 mpg).
3. Calculate the t-statistic using the sample mean, population mean, sample standard deviation, and sample size.
4. Compare the calculated t-statistic to the critical t-value from the t-distribution table at the desired confidence level (usually 95%).
5. Decide to reject or fail to reject the null hypothesis based on whether the t-statistic falls in the critical region.