Question

Repeated data on individuals who participated in a randomized experiment are presented below.

Participants	1	2	3	4	5	6	7	8
Assessment I	160	180	200	190	210	180	210	190
Assessment II	200	230	210	235	240	195	230	200

Is the mean difference from this experiment statistically significant? Assume the level of significance is 5%. Use the steps for hypothesis testing and show all your work.

Answer 1

Here, we have to use paired t test.

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

H₀: µ_d = 0 versus H_a: µ_d ≠ 0

This is a two tailed test.

Test statistic for paired t test is given as below:

t = (Dbar - µ_d)/[S_d/sqrt(n)]

From given data, we have

µ_d =0

Dbar = -27.5

S_d = 16.0357

n = 8

df = n – 1 = 7

α = 0.05

t = (Dbar - µ_d)/[S_d/sqrt(n)]

t = (-27.5 - 0)/[ 16.0357/sqrt(8)]

t = -4.8505

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

P-value = 0.0019

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the mean difference is statistically significant at 5% level.