Question

You may need to use the appropriate technology to answer this 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

Ans:

a)

Test statistic:

F=2.2/1.0=2.2

df₁=21-1=20

df₂=26-1=25

p-value(two tailed)=2*FDIST(2.2,20,25)=0.0633

As,p-value>0.05,so

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

b)alpha/2=0.025

critical F values:

FINV(0.025,20,25)=2.30

FINV(0.975,20,25)=0.42

Reject H0,if F<=0.42 or F>=2.30

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