In order to compare the means of two populations, independent random samples of 400 observations are selected from each population, with the following results:
Sample 1 Sample 2
x̄1 = 5,275 .... x̄2 = 5,240
s1 = 150 ...... s2 = 200
a. Use a 95% confidence interval to estimate the difference between the population means (µ1 - µ2). Interpret the confidence interval.
b. Test the null hypothesis H0: (µ1 - µ2) = 0 versus the alternative hypothesis Ha: (µ1 - µ2) ≠ 0. Give the p-value of the test, and interpret the result.
c. Suppose the test in part b were conducted with the alternative hypothesis Ha: (µ1 - µ2) > 0. How would your answer to part b change?
d. Test the null hypothesis H0: (µ1 - µ2) = 25 versus the alternative Ha: (µ1 - µ2) = 25. Give the p-value, and interpret the result. Compare your answer with that obtained from the test conducted in part b.
e. What assumptions are necessary to ensure the validity of the inferential procedures applied in parts a–d?