Two independent random samples have been selected, 100 observations from population 1 and 100 from population 2. Sample means x̄1 = 70 and x̄2 = 50 were obtained. From previous experience with these populations, it is known that the variances are σ12 = 100 and σ22 = 64.
a. Find σ(x̄1 - x̄2).
b. Sketch the approximate sampling distribution (x̄1 - x̄2), assuming that (µ1 - µ2) = 5.
c. Locate the observed value of (x̄1 - x̄2) on the graph you drew in part b. Does it appear that this value contradicts the null hypothesis H0: (µ1 - µ2) = 5?
d. Use the z -table to determine the rejection region for the test of H0: (µ1 - µ2) = 5 against Ha: (µ1 - µ2) = 5. Use α = .05.
e. Conduct the hypothesis test of part d and interpret your result.
f. Construct a 95% confidence interval for (µ1 - µ2). Interpret the interval.
g. Which inference provides more information about the value of (µ1 - µ2), the test of hypothesis in part e or the confidence interval in part f?