Insurance Companies Track Life Expectancy Information to Assist in Determining $78.6$

Multiple Choice

Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Last year the average life expectancy of all policyholders was 77 years. ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample 20 of their recently paid policies. The sample has a mean of $78.6$ years and a standard deviation of $4.48$ years. The $\mathrm { P }$ -value associated with the resulting test statistic is $0.063$ . At $\alpha = 0.05$ , which of the following is the correct conclusion?
I. We fail to reject the null hypothesis.
II. We reject the null hypothesis.
III. There is not significant evidence to indicate an increase in average life expectancy.

A) I only
B) II only
C) III only
D) Both I and III
E) Both II and III