Question

A group of eight individuals with high cholesterol levels were given a new drug that was designed to lower cholesterol levels. Cholesterol levels, in mg/dL, were measured before and after treatment for each individual, with the following results:

Subject	Before	After
1	283	215
2	299	206
3	274	179
4	284	212
5	240	178
6	275	212
7	293	192
8	277	196

Can you conclude that the mean cholesterol level after treatment is less than the mean before treatment? Find the P-value and state a conclusion.

Since  (Click to select)  0.005 < P < 0.01  0.05 < P < 0.10  0.001 < P < 0.005  0.01 < P < 0.025  0.0005 < P < 0.001  P > 0.40  0.25 < P < 0.40  0.025 < P < 0.05  P < 0.0005  0.10 < P < 0.25  , we  (Click to select)  can  cannot  conclude that the mean cholesterol level after treatment is less than the mean before treatment.

Answer 1

The table given below,

Subject	Before	After	di=Before-After	di^2
1	283	215	68	4624
2	299	206	93	8649
3	274	179	95	9025
4	284	212	72	5184
5	240	178	62	3844
6	275	212	63	3969
7	293	192	101	10201
8	277	196	81	6561
		Sum	635	52057

From table ,

Let ,

The null and alternative hypothesis is

The test is one tailed test.

THe test statistic is ,

Now , df=degrees of freedom=n-1=8-1=7

From t-table , The p-value is ,

p-value < 0.0005

Decision : Here , p-value < 0.05 level of significance.

Conclusion : Hence , we can conclude that the mean cholesterol level after treatment is less than the mean before treatment.