In: Statistics and Probability
The data in this file are the differences in the productivity of workers measured before and 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 |
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.
a) 0.20 approximately is the p-value for the null hypothesis that the training program makes no difference to productivity.
b) No, we accept the null hypothesis using a significance level of 10% and a two-sided alternative hypothesis.
c) The following image explains all,