The Level of Significance of a Statistical Test 5.28 The R&D department of a paint company has developed an additive that it hopes will in- crease 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 y - 33.6 and s = 9.2 a. Is there substantial evidence (a = .01) that the additive reduces the mean ab- sorption from its current value? b. What is the level of significance (p-value) of your test results? 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? d. Estimate the mean absorption using a 99% confidence interval. Is the confidence interval consistent with your conclusions from the test of hypotheses?5.30 A concern to public health officials is whether a concentration of lead in the paint of older homes may have an effect on the muscular development of young children. In order to evaluate this phenomenon, a researcher exposed 90 newly born mice to paint containing a specified amount of lead. The number of Type 2 fibers in the skeletal muscle was determined 6 weeks after exposure. The mean number of Type 2 fibers in the skeletal muscles of normal mice of this age is 21.7. The n = 90 mice yielded y = 18.8, s - 15.3. Is there significant evidence in the data to support the hypothesis that the mean number of Type 2 fibers is different from 21.7 using an a = .05 test