Two independent random samples have been selected, 100 observations from population 1 and 100 from population 2.

Sample means x1 = 60 and x2 = 40 were obtained. From previous experience with these populations, it is known that the variances are s1 2 LO5

= 64 and s2 2

= 100.

a. Find s1x1 - x22.

b. Sketch the approximate sampling distribution 1x1 - x22, assuming that 1m1 - m22 = 5.

c. Locate the observed value of 1x1 - x22 on the graph you drew in part

b. Does it appear that this value contradicts the null hypothesis H0: 1m1 - m22 = 5?

d. Use the z-table to determine the rejection region for the test of H0: 1m1 - m22 = 5 against Ha: 1m1 - m22  5.

Use a = .05.

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

f. Construct a 95% confidence interval for 1m1 - m22.

Interpret the interval.

g. Which inference provides more information about the value of 1m1 - m22, the test of hypothesis in part e or the confidence interval in part f?