Question

1. Please provide a detailed description of an original example (i.e., something not discussed in class or the textbook) of a situation in which a paired samples t-test would be most appropriate.

Answer 1

Paired samples uses two groups where the subjects studied are the same. The first groups represents the area of study values before an experiment and the 2nd group represents the area of study values after the experiment. The difference in their means are compared and tested whether the difference is significantly equal to zero as we would have assumed to be or not.

Example:

In an organisation the sales department wants to check whether the employees will generate more sales after a training program or not. Based on a sample he would conduct the test.If the test results in favourable result the department will train all the employees.

Assumptions:

• The samples are randomly selected.
• The samples are independent of each other.
• The sample comes from a normal population.

A sample of sales done by 30 employees over a week has been recorded from XYZ organisation. Later next week the training sessions go on for a week. In the 3rd week again the sales by the same employees are recorded.

Employee	Before training	After training	Difference	Absolute diff (D)
1	24	38	14	14
2	27	25	-2	2
3	38	49	11	11
4	30	43	13	13
5	38	44	6	6
6	40	55	15	15
7	26	39	13	13
8	36	47	11	11
9	20	35	15	15
10	21	33	12	12
11	34	41	7	7
12	30	42	12	12
13	27	40	13	13
14	26	37	11	11
15	35	46	11	11
16	22	19	-3	3
17	28	41	13	13
18	20	32	12	12
19	33	43	10	10
20	22	34	12	12
21	32	40	8	8
22	36	46	10	10
23	39	49	10	10
24	23	38	15	15
25	24	38	14	14
26	26	36	10	10
27	34	39	5	5
28	34	46	12	12
29	31	41	10	10
30	26	40	14	14

Here the paired t-test would be most appropriate because we are testing whether the training has increased sales or not that is is the mean difference (After training - before traing) > 0. The same subejcts are there in the both the groups. The sample is also large. We could conduct a 1-tailed t-test for testing the claim.