Question

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.

A State the null and alternative hypotheses.
B Is this a right-tailed, left-tailed, or two-tailed test?
C In words, define the random variable of interest for this test.
D Which distribution (normal or Student’s t) would you use for this hypothesis test?

Answer 1

Answer)

A)

Null hypothesis Ho : u1 = u2

Alternate hypothesis Ha : u1 not equal to u2

Where, u1 = mean life span for whites

u2 = mean life span for non whites

B)

It is a two tailed test

{Not equal to claim means two tailed, while greater than or less than are one tailed}

C)

Random variable of interest is mean life span of whites and non whites

D)

As the population standard deviations are unknown and we are using sample s.d as the best estimate

We will use students t table to conduct the test