Question

Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations.

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

Subject A B C D E F G

Before: 182 178 199 194 151 188 170

After: 175 169 197 199 137 190 158

Using a 0.01 level of significance, test the claim that the diet is effective in reducing weight

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: the diet is not effective in reducing weight.

Alternative hypothesis: Ha: the diet is effective in reducing weight.

H0: µd = 0 versus Ha: µd > 0

This is a right tailed test.

We take difference as before minus after.

Test statistic for paired t test is given as below:

t = (Dbar - µd)/[Sd/sqrt(n)]

From given data, we have

µd = 0

Dbar = 5.2857

Sd = 7.1581

n = 7

df = n – 1 = 6

α = 0.01

t = (Dbar - µd)/[Sd/sqrt(n)]

t = (5.2857 - 0)/[ 7.1581/sqrt(7)]

t = 1.9537

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

P-value = 0.0493

P-value > α = 0.01

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the diet is effective in reducing weight.