Two independent random samples have been selected.

100 observations from population 1 and 100 from population 2. Sample means T, = 15.5 and ?, = 26.6 were obtained. From previous experience with these populations, it is known that the variances are cr? = 9 and a; = 16.

a. Find u(,,-,).

b. Sketch the approximate sampling distribution for (TI - &) assuming (pl - p2) = 10.

c. Locate the observed value of (il - &) on the graph you drew in part

b. Does it appear that this value contradicts the null hypothesis H,,: (P, - P~) = 10?

d. Use the z-table on the inside of the front cover to determine the rejection region for the test of H,:
(p, - p,) = 10 against H,: (p, - p,) i 10. Use a = .05.

e. Conduct the hypothesis test of part d and interpret your result.

f. Construct a 95% confidence interval for (pl - 4.
Interpret the interval.
g. Which inference provides more information about the value of (p, - p2)-the test of hypothesis in part e or the confidence interval in part f?