Chapter 5.12, Problem 28E

The R&D department of a paint company has developed an additive that it hopes will increase the ability of the company’s stain for outdoor decks to resist water absorption. The current formulation of the stain has a mean absorption rate of 35 units. Before changing the stain, a study was designed to evaluate whether the mean absorption rate of the stain with the additive was decreased from the current rate of 35 units. The stain with the additive was applied to 50 pieces of decking material. The resulting data were summarized to $\bar{y}$ = 33.6 and s = 9.2

1. a. Is there substantial evidence (α = .01) that the additive reduces the mean absorption from its current value?
2. b. What is the level of significance (p-value) of your test results?
3. c. What is the probability of a Type II error if the stain with the additive in fact has a mean absorption rate of 30?
4. d. Estimate the mean absorption using a 99% confidence interval. Is the confidence interval consistent with your conclusions from the test of hypotheses?