Question

conduct your own example of a related-samples t-test.

IV:

level 1:

level 2:

DV:

Answer 1

Let's conduct a paired-samples or related sample t-test. We need to test whether eating corn flakes lowered the cholesterol levels. 20 individuals were assigned a diet randomly that was either oats of corn flakes. After a period of one week on the initial diet, the levels were measured and the other diet was given. After another week, the levels were measured.

IV: Type of Diet
Level 1: Oats
Level 2: Corn Flakes
DV: Cholesterol levels

The data is:

ID	Corn (mmol/L)	Oats (mmol/L)
1	6.84	4.60
2	7.78	4.97
3	4.78	5.69
4	4.35	7.64
5	7.96	3.96
6	3.85	7.85
7	6.80	7.53
8	6.44	6.45
9	7.16	7.51
10	5.00	3.39
11	3.38	6.63
12	3.26	5.76
13	4.25	4.10
14	3.45	3.26
15	7.83	3.85
16	6.55	6.83
17	5.28	4.16
18	5.67	3.33
19	3.85	5.76
20	3.73	6.42

The hypothesis is:

Ho: ud = 0

Ha: ud > 0

The calculations are:

ID	Corn (mmol/L)	Oats (mmol/L)	Difference, d = Corn - Oats
1	6.84	4.60	2.24
2	7.78	4.97	2.81
3	4.78	5.69	-0.90
4	4.35	7.64	-3.29
5	7.96	3.96	3.99
6	3.85	7.85	-4.00
7	6.80	7.53	-0.73
8	6.44	6.45	0.00
9	7.16	7.51	-0.35
10	5.00	3.39	1.60
11	3.38	6.63	-3.25
12	3.26	5.76	-2.50
13	4.25	4.10	0.15
14	3.45	3.26	0.18
15	7.83	3.85	3.98
16	6.55	6.83	-0.28
17	5.28	4.16	1.12
18	5.67	3.33	2.33
19	3.85	5.76	-1.91
20	3.73	6.42	-2.69
		Average	-0.07
		Standard Deviation	2.41

t-statistic = (u - u0)/(s/√n)

= (-0.07 - 0)/(2.41/√20)

t = -0.13

p-value (one-tailed) at df = 20 - 1 = 19 is: 0.449

As the p-value = 0.449 > 0.05, we fail to reject Ho.

We conclude that we do not have sufficient evidence to say that eating corn flakes lowered the cholesterol levels significantly