Question

Sample 1: 1, 2, 3, 4, 5

Sample 2: 2, 4, 6, 8, 10

Use this data to conduct the paired test with a significance level of 0.05. Select the appropriate conclusion below.

-Fail to reject the null hypothesis

-Accept null hypothesis

-Reject null hypothesis

-Unable to reject or fail to reject

Answer 1

Here, we have to use paired t test.

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

H0: µd = 0 versus Ha: µd ≠ 0

This is a two tailed test.

We take differnece as sample 2 minus sample 1.

Test statistic for paired t test is given as below:

t = (Dbar - µd)/[Sd/sqrt(n)]

From given data, we have

Dbar = 3

Sd = 1.5811

n = 5

df = n – 1 = 4

α = 0.05

t = (Dbar - µd)/[Sd/sqrt(n)]

t = (3 – 0)/[ 1.5811/sqrt(5)]

t = 4.2426

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

P-value = 0.0132

P-value < α = 0.05

So, we reject the null hypothesis

Answer:

-Reject null hypothesis