In 2000 the Census Bureau reported that the average life expectancy for a person in the U.S.A. had increased to 77 years. Insurance companies track life expectancy information in order to determine their premiums for the life insurance policies that they issue. A given insurance company wants to know if its policyholders are also now living longer, so it randomly samples some of the recently paid policies to see if the mean life expectancy of those policyholders has increased. The company plans to change its premium structure only if there is evidence that people who buy insurance from the company are living longer than before. Here are the results of the random survey:
Age at death of 20 policyholders
|
86
|
75
|
83
|
84
|
81
|
77
|
78
|
79
|
79
|
81
|
|
76
|
85
|
70
|
76
|
79
|
81
|
73
|
74
|
72
|
83
|
Does this sample indicate that the company should change its premium structure?
For more accurate calculations, the insurance company wants to estimate the life expectancy to within 1 year (margin of error) with 95% confidence. How many randomly selected records would they need to examine?