The mean drying time of a brand of spray paint is known to be 90 seconds. The research division of the company that produces this paint contemplates that adding a new chemical ingredient to the paint will accelerate the drying process. To investigate this conjecture, the paint with the chemical additive is sprayed on 15 surfaces and the drying times are recorded. The mean and the standard deviation computed from these measurements are 86 and 4.5 seconds, respectively.
(a) Do these data provide strong evidence that the mean drying time is reduced by the addition of the new chemical?
(b) Construct a 98% confidence interval for the mean drying time of the paint with the chemical additive.
(c) What did you assume about the population distribution?