Question

The data in this file are the differences in productivity of workers measured before and after they undertake a training program.

1. Compute the p-value for the null hypothesis that the training program makes no difference to productivity.
2. Using a significance level of 5% and a two-sided alternative hypothesis, do you reject H0?
3. Do you need to make any assumptions in order for your test to be valid?

In your answer, you should state the null and alternative hypotheses, the significance level, the PDF of the test statistic under the null hypothesis, the value of the test statistic, the p-value, and your conclusion.

x
2.484167
2.622733
-0.75935
6.140174
-0.17906
3.986727
-1.53426
2.578041
-0.27519
-1.26048
-1.1097
1.026746
1.314893
2.821092
2.122202
0.570733
0.153999
0.783752
3.000589
1.58411
1.271098
1.011011
1.379925
1.726544
2.517921
1.377871
2.872509
1.181797
2.969338
0.828915
-0.79228
1.053184
0.696111
-0.23973
1.254516
0.870221
0.240092
0.725512
1.677367
1.103163
2.555754
1.328298
-0.21676
1.984989
0.886859
2.980936
1.954234
0.655308
0.599596
2.534806
0.543636
0.190243
2.51095
2.887347
0.428632
1.585644
1.294086
2.994844
1.039462
0.167443
2.095357
1.321115
0.889275
0.703562
1.235611
2.705786
-0.4321
0.854645
1.223376
1.172388
2.540959
3.054705
0.353152
0.501281
2.717594
2.170033
3.274171
2.233734
1.49754
3.892104
2.160767
0.972804
2.329182
2.001422
0.686487
2.877506
2.554813
1.572571
-0.40125
1.893989
1.956781
0.972992
1.031437
1.237951
1.278917
1.436277
0.270507
0.385386
2.323071
-0.31962
1.786228
4.005211
1.209229
0.293988
2.899336
0.26951
1.241443
2.009414
-1.10836
1.282146
1.96603
4.345526
2.018346
2.725603