Question

Stable cost reporting in a manufacturing setting is typically a sign that operations are running smoothly. The accounting department analyzes the variance of the weekly costs reported by two of its production departments. A sample of 16 cost reports for each of the two departments shows cost variances of 2.7 and 5.5, respectively. Is this sample sufficient to conclude that the two production departments differ in terms of weekly cost variance? Use

α = 0.10.

State the null and alternative hypotheses.

H₀: σ₁² > σ₂²

H_a: σ₁² ≤ σ₂²

H₀: σ₁² ≠ σ₂²

H_a: σ₁² = σ₂²

H₀: σ₁² ≤ σ₂²

H_a: σ₁² > σ₂²

H₀: σ₁² = σ₂²

H_a: σ₁² ≠ σ₂²

Find the value of the test statistic. (Round your answer to two decimal places.)

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

p-value =

State your conclusion.

Do not reject H₀. We cannot conclude that there is a difference between the population variances.

Reject H₀. We can conclude that there is a difference between the population variances.    

Reject H₀. We cannot conclude that there is a difference between the population variances.

Do not reject H₀. We can conclude that there is a difference between the population variances.

Answer 1

H0: σ12 = σ22

Ha: σ12 ≠ σ22

Test Statistic :-

f = 2.7 / 5.5
f = 0.49

P value = 2 * P ( f > 0.4909 ) = 0.1798

Reject null hypothesis if P value < α = 0.10
Since P value = 0.1798 > 0.10, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Do not reject H0. We cannot conclude that there is a difference between the population variances.