The mean drying time of a certain paint in a certain application is 12 minutes. A new additive will be tested to see if it reduces the drying time. One hundred specimens will be painted, and the sample mean drying time X will be computed. Assume the population standard deviation of drying times is ???? = 2 minutes.

Let ???? be the mean drying time for the new paint.

The null hypothesis H0 : ???? ≥ 12 will be tested against the alternate H1 : ???? < 12. Assume that unknown to the investigators, the true mean drying time of the new paint is 11.5 minutes.

a. It is decided to reject H0 if X ≤ 11.7. Find the level and power of this test.

b. For what values of X should H0 be rejected so that the power of the test will be 0.90? What will the level then be?

c. For what values of X should H0 be rejected so that the level of the test will be 5%? What will the power then be?

d. How large a sample is needed so that a 5% level test has power 0.90?