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 Wib be Worker i's wage under the old management and let Wii be Worker i's wage after the change. The difference is Assume that the Di are a random sample from a Normal 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(Di) under H0? If you are hired to examine the validity of the new management's claim, what is the relevant alternative hypothesis in terms of ?

(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).