Question

Group A	Group B
1	5
5	8
5	6
5	7
5	8
6	8
7	9
6	16
10	20
13	24

At the significance level of 0.05, are the drug concentrations in Group A and Group B different? Using the most appropriate t test.

Answer 1

Solution:

Here, we have to use two sample t test for the difference in two population means by assuming equal population variances.

H₀: µ₁ = µ₂ versus H_a: µ₁ ≠ µ₂

This is a two tailed test.

Test statistic formula for pooled variance t test is given as below:

t = (X1bar – X2bar) / sqrt[S_p²*((1/n1)+(1/n2))]

Where S_p² is pooled variance

S_p² = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)

From given data, we have

X1bar = 6.3

X2bar = 11.1

S1 = 3.233505

S2 = 6.52261

n1 = 10

n2 = 10

df = n1 + n2 – 2 = 10 + 10 – 2 = 18

α = 0.05

Critical value = - 2.1009 and 2.1009

(by using t-table)

S_p² = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)

S_p² = [(10 – 1)* 3.233505^2 + (10 – 1)* 6.52261^2]/(10 + 10 – 2)

S_p² = 26.5

t = (X1bar – X2bar) / sqrt[S_p²*((1/n1)+(1/n2))]

t = (6.3 – 11.1) / sqrt[26.5*((1/10)+(1/10))]

t = -4.8/2.3022

t = -2.0850

P-value = 0.0516

(by using t-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is insufficient evidence to conclude that the drug concentrations in Group A and Group B are different.