Question

The table below shows the weights of 9 subjects before and after following a particular diet for two months.

Subject	A	B	C	D	E	F	G	H	I
Before	168	180	157	132	202	124	190	210	171
After	162	178	145	125	171	126	180	195	163

Use a 0.01 significance level to test the claim that the particular diet is effective in reducing subjects' weights.

Answer 1

Here, we have to use paired t test.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: Diet is not effective in reducing subjects' weights.

Alternative hypothesis: H_a: Diet is effective in reducing subjects' weights.

H₀: µ_d = 0 versus H_a: µ_d > 0

This is a right tailed test.

We take the difference as before minus after.

Test statistic for paired t test is given as below:

t = (Dbar - µ_d)/[S_d/sqrt(n)]

From given data, we have

µ_d = 0

Dbar = 9.8889

S_d = 9.4001

n = 9

t = (Dbar - µ_d)/[S_d/sqrt(n)]

t = (9.8889 - 0)/[ 9.4001/sqrt(9)]

t = 3.1560

df = n – 1 = 9 - 1 = 8

α = 0.01

The p-value by using t-table is given as below:

P-value = 0.0067

P-value < α = 0.01

So, we reject the null hypothesis

There is sufficient evidence to conclude that Diet is effective in reducing subjects' weights.