Question

Did these four students show significant improvement over time? Provide your conclusion with quantitative evidence or show your calculation in your short answer.

Pretest	Posttest	Improvement
30	35	5
40	42	2
40	45	5
50	54	4

Answer 1

Solution:

Here, we have to use paired t test.

H₀: µ_d = 0 versus H_a: µ_d > 0

Test statistic for paired t test is given as below:

t = (Dbar - µ_d)/[S_d/sqrt(n)]

From given data, we have

Dbar = 4

S_d = 1.414213562

n = 4

df = n – 1 = 3

We assume α = 0.05

Critical value = 2.3534

(by using t-table)

t = (4 – 0)/[ 1.414213562/sqrt(4)]

t = 4/0.7071

t = 5.6569

P-value = 0.0055

(by using t-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the students show significant improvement over time.