An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and a 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 are shown here. What is the value of the test statistic?
A)1.943
B)1.895
C)2.542
D)2.447

Question

An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and a 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 are shown here.  What is the value of the test statistic?
A)1.943 
B)1.895 
C)2.542 
D)2.447

Quizplus · Accepted Answer

To calculate the test statistic, we need to find the mean and standard deviation of the differences in scores:

Mean difference = (15-7) + (10-8) + (20-18) + (13-10) + (17-14) + (11-9) + (16-12) / 7 = 2.57

Standard deviation of the difference = sqrt(((15-7-2.57)^2 + (10-8-2.57)^2 + (20-18-2.57)^2 + (13-10-2.57)^2 + (17-14-2.57)^2 + (11-9-2.57)^2 + (16-12-2.57)^2)/6) = 3.39

The test statistic is then calculated as:

t = (2.57 - 0) / (3.39 / sqrt(7)) = 2.542

Therefore, the answer is C: 2.542.

An Investigation of the Effectiveness of a Training Program to Improve