Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Last year the average life expectancy of all policy holders was 77 years. ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample some of their recently paid policies. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. The sample has a mean of 78.6 years and a standard deviation of 4.48 years.
a. Write the null and alternative hypotheses.
b. In this context, describe the Type I error possible. How might such an error impact ABI Insurance?
c. In this context, describe the Type II error possible. How might such an error impact ABI Insurance?
d. What is the value of the test statistic?