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 processof examining several pension plans. Because the length of life of the pension plan holders iscritical 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 meanage 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 withα = .05 that there is evidence to indicate the mean age of retirees has increasedsince 1991? Provide both rejection region and p-value.