Question

Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, 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 whites and nonwhites.

In words, define the random variable of interest for this test.

Short answer

The disparity in mean life lengths between whites and nonwhites is a random variable of interest for this test.

Step-by-step solution

Given information

The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, 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 whites and nonwhites.

Define the random variable of interest for this test in words.

The difference between the mean life lengths of whites and nonwhites, which is represented by ${\overline{X}}_W-{\overline{X}}_{NW}$, is the random variable of interest for this test.

The average lifespan of white people is${\overline{X}}_W$.

Nonwhites have a life expectancy of ${\overline{X}}_{NW}$.