Introductory Econometrics 4th Edition by Jeffrey Wooldridge

Exercise 9

The new management at a bakery claims that workers are now more productive than they were under old management, which is why wages have "generally increased." Let Wi b be Worker i's wage under the old management and let Wi a be Worker i's wage after the change. The difference is D i = W i a - W i b. Assume that the D i are a random sample from a Normal( , 2 ) distribution.
(i) Using the following data on 15 workers, construct an exact 95% confidence interval for .
(ii) Formally state the null hypothesis that there has been no change in average wages. In particular, what is E(D i ) under H 0 If you are hired to examine the validity of the new management's claim, what is the relevant alternative hypothesis in terms of =E(D i )
(iii)Test the null hypothesis from part (ii) against the stated alternative at the 5% and 1% levels.
(iv) Obtain the p-value for the test in part (iii).