A statistical analyst who works for a large insurance company is in the process of examining several pension plans. Because the...

A statistical analyst who works for a large insurance company is in the process
of examining several pension plans. Because the length of life of the pension plan holders is
critical to the plans’ integrity, the analyst needs to know if the mean age has changed. In the last census (1991), suppose the mean age of retirees is 67.5. To determine whether the mean
age has increased, the analyst selects a random sample of 100 retirees and finds that ¯x = 68.2.
If we assume that the population standard deviation is σ = 3.1, can we conclude with
α = .05 that there is evidence to indicate the mean age of retirees has increased
since 1991? Provide both rejection region and p-value.