The life insurance industry maintains that the average worker in Saskatoon has no more than $25,000 of personal life insurance. You believe it is higher. You sample 100 workers in Saskatoon at random and find the sample average to be $26,650 of personal life insurance. The population standard deviation is known to be $12,000. Use α=0.05 throughout.
a. Test your belief using a significance level of 5%.
b. Explain, in the context of this question, what is meant by a Type I error, a Type II error, and the power of the test?
c. If the true average for this population is in fact $30,000, what is the probability of committing a Type II error?
d. Calculate the power of the test.