Life insurance experts have been claiming that the average 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 interviews 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.

a. 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.

b. If the actual average for this population is $30,000, what is the probability of committing a Type II error?