One of the key factors in concrete work is the time it takes for the concrete to “set up.” Suppose a concrete supplier 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 are observed:

Old Additive New Additive x = 17.2 hours x = 15.9 hours s = 2.5 hours s = 1.8 hours

a. Use these sample data to construct a 90% confidence interval estimate for the difference in mean setup times 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 with equal variances.) 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 the average setup time?