Question

Consider the following hypothesis test.

H₀: σ₁² = σ₂²

H_a: σ₁² ≠ σ₂²

(a) What is your conclusion if n₁ = 21, s₁² = 8.2, n₂ = 26,  and s₂² = 4.0? Use α = 0.05 and the p-value approach

Find the value of the test statistic.

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Reject H₀. We cannot conclude that σ₁² ≠ σ₂².

Do not reject H₀. We cannot conclude that σ₁² ≠ σ₂².  

  Reject H₀. We can conclude that σ₁² ≠ σ₂².

Do not reject H₀. We can conclude that σ₁² ≠ σ₂².

(b) Repeat the test using the critical value approach.

Find the value of the test statistic.

State the critical values for the rejection rule. (Round your answers to two decimal places. If you are only using one tail, enter NONE for the unused tail.)

test statistic≤

test statistic≥

State your conclusion.

Reject H₀. We cannot conclude that σ₁² ≠ σ₂².

Do not reject H₀. We cannot conclude that σ₁² ≠ σ₂².   

Reject H₀. We can conclude that σ₁² ≠ σ₂².

Do not reject H₀. We can conclude that σ₁² ≠ σ₂².

Answer 1

Part a)

Test Statistic :-

f = 8.2 / 4
f = 2.05

P value = 2 * P ( f > 2.05 ) = 0.9548

Reject null hypothesis if P value < α = 0.05
Since P value = 0.9548 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Do not reject H₀. We cannot conclude that σ₁² ≠ σ₂².

Part b)

Test Statistic :-

f = 8.2 / 4
f = 2.05

Critical values are

f(0.05/2 , 20 , 25 ) = 2.3005 ≈ 2.30
f(1 - 0.05/2 ,20 , 25 ) = 0.4174 ≈ 0.42

Reject null hypothesis if f > f(α/2,n1-1,n2-1) OR f < f(1 - α/2), n1-1 , n2-1)

2.05 lies between the value 2.3005 and 0.4174 , hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Do not reject H₀. We cannot conclude that σ₁² ≠ σ₂².