x -0.589195516 -1.165999365 -1.196664499 -1.257563483 -0.525990202 0.854812885 -0.793681837 -1.417444643 -0.587108308 -0.858825728 -0.701407141 -1.422989542 0.599696525 -1.284589636 -1.001937874...

x
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There are 118 values that show the differences in productivity of workers measured before and after they undertake a training program.

Test the null hypothesis that the training program makes no difference to productivity against a two-sided alternative hypothesis using a significance level of 5%. 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, and your conclusion.
Do you need to make any assumptions in order for your test to be valid?

Expert Solution

The null hypothesis is: There is no difference in productivity pre and post training program

The alternate hypothesis is: There is difference in productivity pre and post training program

The level of significance is 5%

Since, the difference figures are provided, use t-test.

Had the pre & post figures were provided, paired t test would have been used.

The test result is:

The degree of freedom = n-1 = 117

At 5% level of significance, the critical t-statistic for two-tailed is given as 1.96

Since, the critical t-statistic is less than actual t-statistic of 8.32968 at 5% level of significance and at 117 degree of freedom, the null hypothesis is rejected.

This implies, there is statistically significant difference between pre and post training program on productivity.

The assumption that is made is that the series of values showing productivity is continuous & normally distribution.

Rahul Sunny answered 1 year ago

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