An ambitious young worker claims that older employees have a better chance of being CEOs than younger employees. To confirm this, he sampled the ages of CEOs for 31 companies. The mean age in the sample was found to be 41.77, with a standard deviation of 10.24 (based on data from Profit, May 29, 1996). If the mean age for all workers in the population is 37, and if the significance level 0.01 is used, test the hypothesis that the CEOs have a higher mean age than workers in general. Explain how your answer to this question relates to the young worker's original claim-that older employees have a better chance of being CEO.