Five new paint additives have been tested to see if any of them can reduce the mean drying time from the current value of 12 minutes. Ten specimens have been painted with each of the new types of paint, and the drying times (in minutes) have been measured. The results are as follows:

Additive ABCDE 1 14.573 10.393 15.497 10.350 11.263 2 12.012 10.435 9.162 7.324 10.848 3 13.449 11.440 11.394 10.338 11.499 4 13.928 9.719 10.766 11.600 10.493 5 13.123 11.045 11.025 10.725 13.409 6 13.254 11.707 10.636 12.240 10.219 7 12.772 11.141 15.066 10.249 10.997 8 10.948 9.852 11.991 9.326 13.196 9 13.702 13.694 13.395 10.774 12.259 10 11.616 9.474 8.276 11.803 11.056 For each additive, perform a hypothesis test of the null hypothesis H0 : ???? ≥ 12 against the alternate H1 : ???? < 12. You may assume that each population is approximately normal.

a. What are the P-values for the five tests?

b. On the basis of the results, which of the three following conclusions seems most appropriate?

Explain your answer.

i. At least one of the new additives results in an improvement.

ii. None of the new additives result in an improvement.

iii. Some of the new additives may result in improvement, but the evidence is inconclusive.