Question

You may need to use the appropriate technology to answer this 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

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

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

p-value =

Answer 1

   Sample 1:  
Sample Variance,    s₁² =    0.0489
Sample size,    n₁ =    25

   Sample 2:  
Sample variance,    s₂² =    0.0058
Sample size,    n₂ =    22
   α =    0.05

1)

Null and alternative hypothesis:  
Hₒ : σ₁² = σ₂²  
H₁ : σ₁² ≠ σ₂²  
Test statistic:  
F = s₁² / s₂² = 0.048889 / 0.0058 =    8.42

2)

Degree of freedom:  
df₁ = n₁-1 =    24
df₂ = n₂-1 =    21
P-value :  
P-value = 2*F.DIST.RT(8.4163, 24, 21) =    0.0000
Conclusion:  
As p-value < α, we reject the null hypothesis.