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. (Let w = white, and nw = nonwhite.) H0: μw = μnw Ha: μw > μnw H0: μw = μnw Ha: μw ≠ μnw H0: μw ≠ μnw Ha: μw = μnw H0: μw = μnw Ha: μw < μnw (b) In symbols, what is the random variable of interest for this test? (Let w = white, and nw = nonwhite.) μw − μnw Xw − Xnw SE xd pc (c) The standard error of (Xw − Xnw) equals (Round to 3 decimal

Answer 1

Explanation:

Let w = white

Let nw = nonwhite

a) We would set up the hypothesis

For the null hypothesis,

H0: μw = μnw

For the alternative hypothesis,

Ha: μw ≠ μnw

This is a two tailed test

b) Random variable = xw - xnw = difference in the sample mean life span of whites and nonwhites born in 1990

c) The standard error formula is

Standard error = √s1²/n1 + s2²/n2

Where

s1 and s2 are the sample standard deviations

n1 and n2 are the number of samples

From the information given,

s1 = 12.7

s2 = 15.6

n1 = 124

n2 = 82

The standard error of (Xw − Xnw)

= √12.7²/124 + 15.6²/82

= √1.3 + 2.97

= 2.07