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?
