Question

Consider the following hypothesis test. H0: σ12 = σ22 Ha: σ12 ≠ σ22 (a) What is...

Consider the following hypothesis test.

H0: σ12 = σ22

Ha: 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.

Homework Answers

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.   

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