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.)

State your conclusion.

(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.

Answer 1

b)

a) F = 2.05, df1 = 20, df2 = 25

value of test statistic is 2.05

Right-tail p-value is

2*0.04518

0.090

P values greater than 0.05 so we can not reject null hypothesis.

R command: pf(2.05, 20, 25, lower.tail=FALSE) or 1-pf(2.05, 20, 25)

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