A psychological study found that men who were distance runners
lived, on average, five years longer than those who were not distance
runners. The study was conducted using a random sample of 50 men
who were distance runners and an independent random sample of 30
men who were not distance runners. The men who were distance
runners lived to be 84.2 years old, on average, with a standard
deviation of 10.2 years. The men who were not distance runners lived
to be 79.2 years old, on average, with a standard deviation of 6.8 years.
Which of the following is the test statistic for the appropriate test to
determine if men who are distance runners live significantly longer, on
average, than men who are not distance runners?