Question

A restaurant wants to test the quality of service before training and after training. Their objective is to determine if the training is effective in improving their service standards. The staff were evaluated on a scale of 1 to 10 with1 being very bad and 10 being very good. Using an appropriate test determine if the training was effective in achieving its objective. The following table displays the results of the study: Participant 1 2 3 4 5 6 After training 10 9 9 7 9 8 Before training 8 8 6 8 6 5 di
i)	If di represents the difference in index (after training – before training) for participant i, find di for i = 1,….,6. Using your calculator or otherwise determine the mean, and standard deviation of di.to four decimal places

Answer 1

Given:

= 0.05, n = 6

Computational Table:

After training	Before training	d = After training - Before Training	d2
10	8	2	4
9	8	1	1
9	6	3	9
7	8	-1	1
9	6	3	9
8	5	3	9
Total		11	33

Hypothesis:

.............training was not effective

...........training was effective

Calculation:

Mean of di:

Standard deviation of di:

Test statistic:

Degrees of Freedom = n-1 = 6-1 = 5

Critical value:

.....................Using t table

Conclusion:

Test statistic (t) > Critical value, i.e 2.8031 > 2.0150, That is Reject Ho at 5% level of significance

Therefore, there is sufficient evidence to conclude that the Training was Effective.