Wilson Construction and Concrete Company is known as a very progressive company that is willing to try new ideas to improve its products and service. One of the key factors of importance in concrete work is the time it takes for the concrete to “set up.” The company is considering a new additive that can be put in the concrete mix to help reduce the setup time. Before going ahead with the additive, the company plans to test it against the current additive. To do this, 14 batches of concrete are mixed using each of the additives. The following results were observed:

a. Use these sample data to construct a 90% confidence interval estimate for the difference in mean setup time for the two concrete additives. On the basis of the confidence interval produced, do you agree that the new additive helps reduce the setup time for cement? (Assume the populations are normally distributed.) Explain your answer.
b. Assuming that the new additive is slightly more expensive than the old additive, do the data support switching to the new additive if the managers of the company are primarily interested in reducing average setup time?