In 2000 the Bureau of the Census reports that the average life expectancy for a person in the United States has increased to 77 years. Insurance companies track life expectancy information to assist in determining the cost of the life insurance policies. The insurance company wants to know if their clients have also started living longer, so they contact the great Mr. Wiegner to randomly sample some of the recently paid policies to see if the mean life expectancy of policy holders has also increased. The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before. Of the 20 policies Mr. Wiegner sampled, he found the average age of death was 78.6 years with a standard deviation of 4.477 years. Assume all conditions are met.

Does this sample indicate that the insurance company should increase their premiums? Test appropriate hypotheses state your conclusion at a 10% significance level.