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       3.26

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

Ha: σ12 ≤ σ22

H0: σ12 ≤ σ22

Ha: σ12 > σ22

   

H0: σ12 = σ22

Ha: σ12 ≠ σ22

H0: σ12 ≠ σ22

Ha: 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.

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