Question

A new drug is proposed to lower total cholesterol and a study is designed to evaluate the efficacy of the drug in lowering cholesterol. Fifteen patients agree to participate in the study and each is asked to take the new drug for 6 weeks. However, before starting the treatment, each patient's total cholesterol level is measured. The initial measurement is a pre-treatment or baseline value. After taking the drug for 6 weeks, each patient's total cholesterol level is measured again and the data are shown below.

Initial	Cholesterol
Cholesterol	at Week 6
215	205
190	156
230	190
220	180
214	201
240	227
210	197
193	173
210	204
230	217
180	142
260	262
210	297
190	184
200	193

Based on the scenario above, analyse the data with appropriate statistical methods and describe your findings in details (both descriptive and inferential). Use alpha=0.05

[Hint: while describing inferential use hypothesis, test statistics confidence interval etc.]

Answer 1

First we need to find the differences "d" = initial - week 6

Then we find the mean of the differences

Mean ( )= 164/ 15 = 10.6333

Standard deviation (Sd) = =  

Standard deviation = 30.3279

Claim : A new drug lowers total cholesterol.

: = 0 vs : > 0

Given : = 10.6333 , Sd = 30.3279, n = 15

    t =

t =

t = 1.40

Critical value:  

α = 0.05

As Ha contain > sign , this is one tail test,

df = n - 1 = 15-1 = 14

For one tail test , t(0.05,14 ) = 1.761

Decision :

As test statistic t is less than 1.761 , we fail to reject the null H0

Conclusion : There is no significant evidence that  there is a reduction in cholesterol levels over 6 weeks.