insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Five years ago the average life expectancy of all policyholders was 77 years. ABI Insurance wants to determine if its clients now have a longer life expectancy compared to five years ago, on average, so it randomly samples some of its recently paid policies. The insurance company will only change its premium structure if there is evidence that people who buy their policies now are living longer than they were five years ago. The sample has a mean of 78.6 years and a standard deviation of 4.48 years. A Type II error in this context would be     Failing to detect an increase in the average life expectancy, when in fact it has     Failing to detect an increase in the average life expectancy, when in fact it hasn't     Detecting an increase in the average life expectancy, when in fact it has     Detecting an increase in the average life expectancy, when in fact it hasn't

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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insurance companies track life expectancy information to assist in determining the cost of life insurance policies. Five years ago the average life expectancy of all policyholders was 77 years. ABI Insurance wants to determine if its clients now have a longer life expectancy compared to five years ago, on average, so it randomly samples some of its recently paid policies. The insurance company will only change its premium structure if there is evidence that people who buy their policies now are living longer than they were five years ago. The sample has a mean of 78.6 years and a standard deviation of 4.48 years. A Type II error in this context would be

   
Failing to detect an increase in the average life expectancy, when in fact it has
   
Failing to detect an increase in the average life expectancy, when in fact it hasn't
   
Detecting an increase in the average life expectancy, when in fact it has
   
Detecting an increase in the average life expectancy, when in fact it hasn't
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