Reference no: EM1312039

Hypothesis testing for difference between matched pairs

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 W_i^b, be worker i's wage under the old management and let W_i^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 (µ, σ²) distribution.

(i) Using the following data on 15 workers, construct an exact 95% confidence interval for µ.

(ii) Formally state the null hypothesis that there has been no change in average wages. In particular, what is E(D_i) under H_o? If you are hired to examine the validity of the new management's claim, what is the relevant alternative hypothesis in terms of µ = 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).

Worker	Wage Before	Wage After
1	8.30	9.25
2	9.40	9.00
3	9.00	9.25
4	10.50	10.00
5	11.40	12.00
6	8.75	9.50
7	10.00	10.25
8	9.50	9.50
9	10.80	11.50
10	12.55	13.10
11	12.00	11.50
12	8.65	9.00
13	7.75	7.75
14	11.25	11.50
15	12.65	13.00