The data in this fileare the differences in the productivity of workers measured beforeand after they undertake a training program.

x
3.483286
0.502139
1.182506
-0.78977
-1.23055
0.050956
-0.55935
-0.44297
-0.28723
-2.20755
-1.29574
-2.37856
1.590792
-1.07265
-0.51803
0.88382
-1.20074
-0.37303
0.046192
0.178191
3.011939
0.370306
-1.16088
0.896363
0.921949
-0.79235
-0.65858
1.442165
1.291734
-1.19235
0.77025
0.130772
0.170839
0.424066
0.144973
-2.14435
0.925843
2.61098
1.358568
1.635042
-0.39504
0.493437
-0.12331
-1.35487
0.336548
-2.47492
-2.26872
-0.25936
-0.54652
1.104589
-0.39521
3.072957
1.835252
-1.30094
2.040434
2.496305
0.567188
0.268885
2.94741
-0.68594
0.456223
3.001556
0.13461
1.583389
-2.45525
0.400895
-0.47353
0.125818
1.759114
-1.28538
1.848862
1.660223
1.305507
-0.90777
0.613334
1.93013
-0.65393
1.430928
0.788061
0.914506
-0.43457
-0.30062
1.352496
0.585404
0.425084
1.503991
1.308418
0.96236
1.012683
-1.09146
0.990711
-1.1824
-2.12897
-1.1366
1.619349
1.026202
-1.49041
-1.53156
-1.11697
-1.00746

1. Compute the p-value for the null hypothesis that the trainingprogram makes no difference to productivity.
2. Using a significance level of 10% and a two-sided alternativehypothesis, do you reject H0H0?
3. Do you need to make any assumptions in order for your test tobe valid?

In your answer, youshould state the null and alternative hypotheses, the significancelevel, the PDF of the test statistic under the null hypothesis, thevalue of the test statistic, the p-value, and your conclusion.