Question

Consider the following hypothesis test.

H₀: σ₁² = σ₂²

H_a: σ₁² ≠ σ₂²

(a)

What is your conclusion if

n₁ = 21, s₁² = 2.2, n₂ = 26, and s₂² = 1.0? 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

The statistical software output for this problem is :

(a)

Test statistics = 2.2

P-value = 0.0633

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

(b)

Critical value = 2.3

Test statistic < Critical value

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