Question

Once you have the dataset, please use knowledge gained in other business and/or economics classes to realize what topic and theory the data could relate and a research question that it could allow you to answer. More specifically, please put together an analysis by making sure your project report includes the following

1. Make a decision about the null and research hypothesis by comparing the obtained value to the critical value and interpret the results of the data. You can pay attention also to the p-values.

2. Sum up you research report by relating the statistical test result(s) to the research question and theory that you set to test.

ID	Nr. of units produced before new compensation system	Nr. of units produced after new compensation system
1	20	23
2	6	8
3	12	11
4	34	35
5	55	57
6	43	76
7	54	54
8	24	26
9	33	35
10	21	26
11	34	29
12	33	31
13	54	56
14	23	22
15	33	35
16	44	41
17	65	56
18	43	34
19	53	51
20	22	21
21	34	31
22	32	33
23	44	38
24	17	15
25	28	27
26	47	50
27	35	78
28	29	29
29	36	44
30	25	23

Answer 1

As per the data,

The paired t-test is considered.

Answer 1)

H₀: μ = 0; i.e. there is no difference between the before and after compensation system

H1: μ $\neq$ 0; i.e. the is a significant difference between the before and after compensation system

Id	Nr. of units produced before new compensation system	Nr. of units produced after new compensation system	Difference
1	20	23	-3
2	6	8	-2
3	12	11	1
4	34	35	-1
5	55	57	-2
6	43	76	-33
7	54	54	0
8	24	26	-2
9	33	35	-2
10	21	26	-5
11	34	29	5
12	33	31	2
13	54	56	-2
14	23	22	1
15	33	35	-2
16	44	41	3
17	65	56	9
18	43	34	9
19	53	51	2
20	22	21	1
21	34	31	3
22	32	33	-1
23	44	38	6
24	17	15	2
25	28	27	1
26	47	50	-3
27	35	78	-43
28	29	29	0
29	36	44	-8
30	25	23	2
		mean	-2.06667
		std dev	10.51086
		std error	1.919012

We can make the following calculations using the difference column D:

s.e. = std dev /$\sqrt{n}$ = 10.5108 /$\sqrt{30}$ = 1.919012

t_obs = (x̄ – μ) /s.e. = (-2.0667 – 0) /1.919012 = -1.0769

t_crit = 2.04522

Since t_obs < t_critwe accept the null hypothesis and conclude with 95% confidence that there is no difference between the before and after compensation system. Alternatively, p-value = 0.290 > .05 = α​​​​​​​

t-Test: Paired Two Sample for Means
	Nr. of units produced before new compensation system	Nr. of units produced after new compensation system
Mean	34.43333333	36.5
Variance	190.6678161	292.7413793
Observations	30	30
Pearson Correlation	0.78925579
Hypothesized Mean Difference	0
df	29
t Stat	-1.076943313
P(T<=t) one-tail	0.145191611
t Critical one-tail	1.699127027
P(T<=t) two-tail	0.290383222
t Critical two-tail	2.045229642