The drying time of a certain type of paint under specified test conditions is known to have mean value 75 minutes. Chemists have proposed a new additive designed to decrease average drying time. Because of the expense associated with the additive, evidence should strongly suggest an improvement in average drying time before the additive is adopted-i.e., only if the null hypothesis is rejected will the additive be declared successful and used.
a) Define the parameter of interest and state the relevant hypotheses.
b) For a sample of n = 35 randomly selected observations, x-bar= 72.6 and s = 9. Conduct a hypothesis test for the hypotheses that you stated in part a at (aplha) = 0.05.
c) If x-bar had been 70 minutes instead of 72.6 minutes (assume s = 9 still), would you reach the same conclusion that you did in part b above? Explain. (Support your explanation with statistical evidence.)