Question

please answer this ASAP

The following test has been resulted before and after good diet (LFD) in order to improve the health of people. The weight of five individuals are recorded as shown below: Let μ1 be the initial weight of the individuals without LFD and μ2 be the weight a with LFD:

PERSON        Weight before              Weight after

1                      149                              142     

2                      194                              189

3                      187                              184

4                      196                              190

5                      203                              199

Set a statistical test to determine if the diet is effective at reducing weight. Use a significance level of 1%.

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 at reducing weight.

Alternative hypothesis: Ha: the diet is effective at 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

Dbar = 5

Sd = 1.5811

n = 5

df = n – 1 = 4

α = 0.01

t = (Dbar - µd)/[Sd/sqrt(n)]

t = (5 – 0)/[ 1.5811/sqrt(5)]

t = 7.0711

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

P-value = 0.0011

P-value < α = 0.01

So, we reject the null hypothesis

There is sufficient evidence to conclude that the diet is effective at reducing weight.