Shipments of light bulbs are acceptable to a distributor if the mean life is at least 1000 hours. A random sample of 48 light bulbs is take and a test is to be done at the 1% level of significance. Assume that the population standard deviation is 50 hours. What is the probability of making a Type II error if the "true" mean is 985 hours?
Ho: mu1=mu2
Ha: mu1 not equal to mu2
t=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)=(116900-115700)/sqrt(2300^2/21+1750^2/26)=1.97
Given a=0.05, the critical value is t(0.025, df=n1+n2-2=45)=2.01
Since t=1.97 is less than 2.01, we do not reject HO. So we can not conclude that there is a difference in the asking price in the two cities.