## Description

The mean drying time of paint in a certain application is 12 min. A new

additive is tested to see if it reduces the drying time. One hundred specimens

are painted, and the sample mean drying time ¯y recorded.

Assume that

the population standard deviation of drying time is 2 min. Let µ be the

mean drying time for the new paint. The null hypothesis H0 : µ ≥ 12 is

tested against the alternative H1 : µ < 12. Assume that, unknown to the

investigators, the true mean drying time of the new paint is 11.5 min.

1. It is decided to reject H0 if ¯y ≤ 11.7. Find the significance level and

the power of the test.

2. For what values of ¯y should H0 be rejected so that the power of the

test is 0.90? What then will the significance level be?

3. For what values of ¯y should H0 be rejected so that the significance level

of the test is 5%? What then will the power be?

4. What is the smallest sample size needed for a 5% level test to have

power at least 0.90?