Two Population Means with Unknown Standard Deviations · Exercise 22

The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for White people born in 1900 and 33.0 years for non-White people. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 White people, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 non-White people, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for White and non-White people.

In symbols, what is the random variable of interest for this test?

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Statistics 2e · §10.1 Two Population Means with Unknown Standard Deviations · Exercise 22