Question

The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance.

Machine 1

2.95	3.45	3.50	3.75	3.48	3.26	3.33	3.20
3.16	3.20	3.22	3.38	3.90	3.36	3.25	3.28
3.20	3.22	2.98	3.45	3.70	3.34	3.18	3.35
3.12

Machine 2

3.22	3.30	3.34	3.28	3.29	3.25	3.30	3.28
3.39	3.34	3.35	3.19	3.35	3.05	3.36	3.28
3.30	3.28	3.30	3.20	3.16	3.33

Conduct a statistical test to determine whether there is a significant difference between the variances in the bag weights for two machines. Use a 0.05 level of significance. What is your conclusion?

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 the process variances are significantly different.

Do not reject H₀. We can conclude that the process variances are significantly different.    

Reject H₀. We can conclude that the process variances are significantly different.

Reject H₀. We cannot conclude that the process variances are significantly different.

Which machine, if either, provides the greater opportunity for quality improvements?

Machine 1 offers the best opportunity for process quality improvements.

Machine 2 offers the best opportunity for process quality improvements.    

Neither machine offers an opportunity for process quality improvements.

Answer 1

	n1    =	25
	n2    =	22
df of numerator v1      =		24
df of denominator v2 =		21
s12 =	0.0489
s22 =	0.006

H₀: σ₁² = σ₂²

H_a: σ₁² ≠ σ₂²

from above data:

Test statistic =s12/s22 =

8.15

P value =

0.0000

Reject H₀. We can conclude that the process variances are significantly different.

Machine 2 offers the best opportunity for process quality improvements.