Last year the average life expectancy of all Happy Life policyholders in Ontario at age 65 was 22.3 years (meaning that a person reaching 65 last year was expected to live, on average, until 87.3). Happy Life wants to determine if their clients now have a longer average life expectancy, 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.
a. Write the null and alternative hypotheses for this test:
H0 :
H1 :
b. In this context, describe a Type I error possible. How might such an error impact Happy Life decision regarding the premium structure?
c. In this context, describe a Type II error possible. How might such an error impact Happy Life decision regarding the premium structure?