Question

Given the following matched samples for individuals exercise time before and after taking energey inducing pill.

Individual	Before	After
1	20	22
2	25	23
3	27	27
4	23	20
5	22	25
6	20	19
7	17	18

If the hypothesis is that the pill increase the individuals exercise time, the p-value at 99% confidence level for data in Exhibit 2 is?

Answer 1

Solution:

Here, we have to use paired t test.

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

Null hypothesis: H0: the pill do not increase the individuals exercise time.

Alternative hypothesis: Ha: the pill increase the individuals exercise time.

H0: µd = 0 versus Ha: µd > 0

This is a right tailed test.

We take difference as after minus before.

Test statistic for paired t test is given as below:

t = (Dbar - µd)/[Sd/sqrt(n)]

From given data, we have

Dbar = 0

Sd = 2.1602

n = 7

df = n – 1 = 6

α = 0.01

t = (Dbar - µd)/[Sd/sqrt(n)]

t = (0 – 0)/[ 2.1602/sqrt(7)]

t = 0.00

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

P-value = 0.5000

P-value > α

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the pill increase the individuals exercise time.