To see if a new training program is effective, you have employees take a pre-tes

Question

To see if a new training program is effective, you have employees take a pre-test before training and a post-test after training. If the post-test scores are significantly improved, you can conclude the training program is effective.

Conduct a hypothesis test for the null hypothesis that there is no significant improvement using the paired t-test with alpha = 0.05.

Use the data in this table:

If you would reject the null hypothesis, enter 1;
If you would fail to reject the null hypothesis, enter 2.

Pre-test Score Post-test Score Improvement 51 59 8 58 83 25 66 51 -15 40 51 11 47 66 19 74 96 22 38 85 47

Explanation / Answer

The statistical software output for the given problem is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between Post-test Score and Pre-test Score
H0 : D = 0
HA : D > 0
Hypothesis test results:

Hence,

Test statistic = 2.345 (Rounded off to 3 decimal places)

Degrees of freedom = 7 - 1 = 6

So critical value for 6 degrees of freedom and 0.05 level of significance = 1.943

Since test statistic exceeds the critical value, reject the null hypothesis. Enter 1

Difference Mean Std. Err. DF T-Stat P-value Post-test Score - Pre-test Score 16.714286 7.1271255 6 2.3451651 0.0287

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