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.)

a) H₀: μ_w ≠ μ_nw
b) H_a: μ_w = μ_nwH₀: μ_w = μ_nw
c) H_a: μ_w < μ_nw    H₀: μ_w = μ_nw
d) H_a: μ_w ≠ μ_nwH₀: μ_w = μ_nw
e) H_a: μ_w > μ_nw

(b) In symbols, what is the random variable of interest for this test? (Let w = white, and nw = nonwhite.)

p_c

x_d    

X_w − X_nw

μ_w − μ_nw

SE

(c) The standard error of (X_w − X_nw) equals
(Round to 3 decimal places)

(d) The P-value is almost 0 for this test. Does it appear that the means are the same? Why or why not?

No, the means appear to be different because the hypothesis test has a p-value less than 0.10.

Yes, the means appear to be different because the hypothesis test has a p-value greater than 0.05.   

No, the means appear to be different because the hypothesis test has a p-value greater than 0.10.

Yes, the means appear to be different because the hypothesis test has a p-value greater than 0.10.

No, the means appear to be different because the hypothesis test has a p-value less than 0.05.

(e) If you were to construct a 95% confidence interval to estimate μ_w - μ_nw, which one of the following about this confidence interval is true?

The confidence interval would contain 0 because the p-value is less than 0.05.

The confidence interval would contain 0 because the p-value is greater than 0.05.     

The confidence interval wouldn't contain 0 because the p-value is less than 0.05.

Answer 1