The drying time of a certain type of paint under specified test
conditions is known to be normally distributed with mean value 75
min and standard deviation 9 min. Chemists have proposed a new
additive designed to decrease average drying time. It is believed
that drying times with this additive will remain normally
distributed with σ = 9. Because of the expense associated with the
additive, evidence should strongly suggest an improvement in
average drying time before such a conclusion is adopted. Let μ
denote the true average drying time when the additive is used. The
appropriate hypotheses are H0: μ = 75 versus Ha: μ < 75.
Consider the alternative value μ = 74, which in the context of the
problem would presumably not be a practically significant departure
from H0. (a) For a level 0.01 test, compute β at this alternative
for sample sizes
n = 144, 784, 2500. (Round your answers to four decimal
places.)
β .8396, ?, .0006
n β
144 .8396
784 ?
2500 .0006