Life insurance experts have been claiming that the aver- age worker in the city of Cincinnati has no more than $25,000 of personal life insurance. An insurance researcher believes that this is not true and sets out to prove that the average worker in Cincinnati has more than $25,000 of personal life insurance. To test this claim, she randomly samples 100 workers in Cincinnati and inter- views them about their personal life insurance coverage. She discovers that the average amount of personal life insurance coverage for this sample group is $26,650. The population standard deviation is $12,000.
Determine whether the test shows enough evidence to reject the null hypothesis posed by the salesperson. Assume the probability of committing a Type I error is .05.
If the actual average for this population is $30,000, what is the probability of committing a Type II error?