Question

Data sets A and B are dependent. Test the claim that the paired sample data is from a population with a mean difference of 0. Use alpha of 0.01.

A	3.2	4.2	6.1	3.1	3.2
B	5.6	4.5	4.4	4.3	5.7

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 paired sample data is from a population with a mean difference of 0.

Alternative hypothesis: Ha: the paired sample data is from a population with a mean difference not equal to 0.

H0: µd = 0 versus Ha: µd ≠ 0

This is a two tailed test.

Test statistic for paired t test is given as below:

t = (Dbar - µd)/[Sd/sqrt(n)]

From given data, we have

Dbar = -0.94

Sd = 1.7329

n = 5

df = n – 1 = 4

α = 0.01

t = (Dbar - µd)/[Sd/sqrt(n)]

t = (-0.94 – 0)/[ 1.7329/sqrt(5)]

t = -1.2129

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

P-value = 0.2919

P-value > α = 0.01

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that the paired sample data is from a population with a mean difference of 0.