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	3.27
3.37	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?

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 =

Answer 1

Given data :

Machine 1 : 2.95,3.45,3.5,3.75,3.48,3.26,3.33,3.2,3.16,3.20,3.22,3.38,3.9,3.36,3.25,3.28,3.2,3.22,2.98,3.45,3.7,3.34,3.18,3.35, 3.12

n₁=25

Mean of mahine1

Sample std dev Machine 1 :

Degrees of freedom Df n=25-1=24

Machine 2 :

3.22,3.3,3.34,3.28,3.29,3.25,3.3,3.27,3.37,3.34,3.35,3.19,3.35,3.05,3.36,3.28,3.3,3.28,3.3,3.2,3.16,3.33
n₂=22

Mean of machine 2 :

Sample std dev Machine 2

Degrees of freedom Df d=22-1=21

Hypothesis:

Test Statistics:

P value : Is the value of the lowets level of singnificance at which we could reject the Null hypothesis H₀
Using P value approch ,we reject the null hypothesis

P value is == 0.00001 almost zero <0.05

Conclusion and decision :

Result is significant at 0.05 Level of singificance

we reject the null hyputhesis,

There is a sufficient evidence that to conclude that singnifice difference between variances of machine