The mean drying time of a brand of spray paint is known to be 90seconds. the research division of the company that produces this paint contemplates that adding a new chemical ingrediant to the pain will accelarate the drying process. To investigate this conjecture, the pain with the chemical additive is sorayed on 15 surfaces and the drying times are recoreded. The mean and standard deviation computed from these measurements are 86 and 4.5 seconds, respectively. assume the measurements consitutes a random sample from a normal population. Do these data provide strong evidence that the mean is drying time is reduced by the addition of the new chemical? to answer this question, perfeom the hypothesis testing ( at the significance level ?=.01) by answering the questions below.

(a) Define the mean in the context of the problem

(b) Formulate the null and alternative hypothesis

(c) State the Type 1 and type 2 error in the context of the probelm

(d) State the test statistic and its disturbution

(e) Determine the critical value for ?=.01 and state the decision rule.

(f) State weather Ho is rejected and tell why.

(h) State your conclusion in words