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 Wibbe be worker i's wage under the old management and let Wia be Worker i's wage after the change. The difference is Di= Wia - Wib . Assume that the Di are a random sample from a normal distribution.

a) using the following data on 15 workers, construct a 95% confidence interval for \mu .

Worker Wage Before Wage After

1 8.3 9.25

2 9.4 9

3 9 9.25

4 10.5 10

5 11.4 12

6 8.75 9.5

7 10 10.25

8 9.5 9.5

9 10.8 11.5

10 12.55 13.1

11 12 11.5

12 8.65 9

13 7.75 7.75

14 11.25 11.5

15 12.65 13

b) 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 managements claim, what is the relavant alternative hypothesis in terms of \mu =E(Di)?

c) Test the null hypothesis from part 2 against the stated alternative of 5% and 1% levels.

d) obtain the p-values for the test in part c