Question

A study was conducted to investigate how effective a new diet was in lowering cholesterol. Results for the

randomly selected subjects are shown in the table. The differences have a normal distribution. Are the subjects’

cholesterol levels lower on average after the diet? Test at the $5\%$level.

Subject	A	B	C	D	E	F	G	H	I
Before	209	210	205	198	216	217	238	240	222
After	199	207	189	209	217	202	211	223	201

Short answer

There is sufficient evidence to conclude that the diet lowers cholesterol.

Step-by-step solution

Given information

Given the results for the randomly selected subjects. Test at $5\%$level.

Calculation

The null and alternative hypothesis are :

$$\begin{gathered} H_0:{\mu }_d=0 \\ {H}_a:{\mu }_d<0 \end{gathered}$$

The significant level, $\alpha =5\%=0.05$.

The p-value is $0.0130$, which is lower than the significant level, so we reject the null hypothesis.

Hence, there is sufficient evidence to conclude that the diet lowers cholesterol.