I think the problem is about whether the program can increase the employee’s motivation. Therefore the hypotheses are better to be set as:

;

. Here one-tail test is chosen.

Upon calculation, assuming the random variable is normally distributed. Then the pooled-variance t-test can be applied with .

Use , where , get , as given in your calculation.

For with , the critical value is .

Therefore we do not reject .

One-tail test and two-tail test differ by the objective: whether you want to see the means are different (two-tail test), or one of the mean is greater than the other (one-tail test).

The p-value (significance probablilty) is the probability of the occurrence of the observed value or more extreme values, given that the null hypothesis holds.

For example, if means if the null hypothesis is true, then there would be only a probability of of observing to be (or greater).

One can compute the p-value to compare with the level of confidence . If the p-value is smaller than , then the null hypothesis is rejected; is not rejected otherwise.

For the critical value, it is used to compare with the z-value, t-value (in this case), value, F-value, etc. In our case, while the t-value is greater than the critical value, then is rejected; is not rejected otherwise.

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Therefore do not worry about tomorrow, for tomorrow will worry about itself. Each day has enough trouble of its own.