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 12.953.453.503.753.483.263.333.203.163.203.223.383.903.363.253.283.203.222.983.453.703.343.183.353.12 Machine 23.223.303.343.283.293.253.303.273.393.343.353.193.353.053.363.283.303.283.303.203.163.33Conduct 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

Answer 1

there is significant difference bag weights for two machines

Explanation:

Given the data :

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 3.27 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

Hypothesis:

H0 : σ1² = σ2²

H1 : σ1² ≠ σ2²

Using calculator, we can obtain the standard deviation of machine 1 and 2 :

Machine 1 : s1 = 0.2211

Machine 2 : s2 = 0.0774

Using the Fratio:

F test = s1² / s2² = 0.2211² / 0.0774² = 8.16

Sample size, n1 = 25 ; n2 = 22

Degree of freedom, n1 - 1 = 25 - 1 = 24 ; n2 - 1 = 22 - 1 = 21

The Pvalue Using the Pvalue from Ftest calculator :

Pvalue < 0.00001

Since Pvalue < α ; We reject the Null and conclude that ; there is significant difference in the bag weights for two machines at 0.05