A company has two factories in which they manufacture engines. Once a month they randomly choose 10 engines from each factory and test if there is difference in performance in engines made in the two factories. This month the average output of motors from Factory 1 is 120 horsepower with the standard deviation of 5 horsepower, and the average output of motors from Factory 2 is 132 horsepower with a standard deviation of 4 horsepower.
(a) Compute a 95% confidence interval for the difference in the average horsepower for engines coming from the two factories and interpret it in context.
(b) Based on your confidence interval, is there a significant evidence that there is a dif- ference in performance in engines made in the two factories? If so, can you tell which factory produces motors with lower performance? Explain.
(c) Recently upgrades were made in Factory 2. Do these data prove that these upgrades enhanced the performance in engines made in this factory? Explain.