An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and post-training customer survey. To compare the differences they computed (post-training survey score - pre-training survey score). Seven customers were randomly selected and completed both surveys. The results follow. For a 0.05 significance level, what is the decision regarding the hypothesis that the training was effective in improving customer relationships?
A) Reject the null hypothesis and conclude that the training was effective.
B) Reject the null hypothesis and conclude that the training was ineffective.
C) Fail to reject the null hypothesis and conclude that the mean survey scores are the same.
D) Fail to reject the null hypothesis and conclude that the mean survey scores are not equal.

Question

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and post-training customer survey. To compare the differences they computed (post-training survey score - pre-training survey score). Seven customers were randomly selected and completed both surveys. The results follow.  For a 0.05 significance level, what is the decision regarding the hypothesis that the training was effective in improving customer relationships?
A) Reject the null hypothesis and conclude that the training was effective. 
B) Reject the null hypothesis and conclude that the training was ineffective. 
C) Fail to reject the null hypothesis and conclude that the mean survey scores are the same. 
D) Fail to reject the null hypothesis and conclude that the mean survey scores are not equal.

Quizplus · Accepted Answer

To determine whether the training program was effective, we need to test the null hypothesis that there is no difference between pre-training and post-training survey scores against the alternative hypothesis that there is a difference. We will use a paired t-test since we have paired data from the same seven customers.

Calculating the differences between the two survey scores:

-1.9, -1.6, -0.9, -1.5, -1.7, -0.6, -2.2

Using a t-test calculator, we find that the t-statistic is -4.161 and the p-value is 0.0034 (assuming a two-tailed test). Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the training was effective in improving customer relationships. Therefore, the correct answer is A.

An Investigation of the Effectiveness of a Training Program to Improve