Answer Happy

2. 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 standard deviation computed from these measurements are 86 and 4.5 seconds, respectively. Assume the measurements constitute a random sample from a normal population. Do these data provide strong evidence that the mean drying time is reduced by the addition of the new chemical? Perform the hypothesis testing at the significance level a = .025) by answering the questions arranged in the following. (a) Define p in the context of this problem. (b) Formulate the null and alternative hypotheses. (c) State the Type I error and Type II error in the context of the problem and tell why Type I error is more serious. (d) State the test statistic and its distribution. (e) Determine the critical value for a = .025 and state the decision rule. (f) Calculate the observed value of the test statistic from the data. (g) State whether Ho is rejected and tell why. (h) Calculate the P-value and do the hypothesis testing based on the P-value. (i) Express the conclusion in the context of the problem, using common language.