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Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in centimeters) are being examined. A random sample of 21roller bearings from the old manufacturing process showed the sample variance of diameters to bes2 = .

Another random sample of27roller bearings from the new manufacturing process showed the sample variance of their diameters to bes2 = .

Use a 5% level of significance to test the claim that there is a difference (either way) in the population variances between the old and new manufacturing processes.

Classify the problem as being a Chi-square test of independence or homogeneity, Chi-square goodness-of-fit, Chi-square for testing or estimatingσ2orσ,Ftest for two variances, One-way ANOVA, or Two-way ANOVA, then perform the following.

One-way ANOVA

Two-way ANOVA

Chi-square test of independence

F test for two variances

Chi-square test of homogeneity

Chi-square goodness-of-fit

Chi-square for testing or estimating σ2 or σ

(i) Give the value of the level of significance. 

State the null and alternate hypotheses. 

H0: σ12 = σ22; H1: σ12 > σ22

H0: σ12 = σ22; H1: σ12 ≠ σ22

H0: σ12 < σ22; H1: σ12 = σ22

H0: σ12 = σ22; H1: σ12 < σ22

(ii) Find the sample test statistic. (Round your answer to two decimal places.) 

(iii) Find the P-value of the sample test statistic. 

P-value > 0.200

0.100 < P-value < 0.200

0.050 < P-value < 0.100

0.020 < P-value < 0.050

0.002 < P-value < 0.020

P-value < 0.002

(iv) Conclude the test. 

Since the P-value is greater than or equal to the level of significance α = 0.05, we fail to reject the null hypothesis.

Since the P-value is less than the level of significance α = 0.05, we reject the null hypothesis.

Since the P-value is less than the level of significance α = 0.05, we fail to reject the null hypothesis.

Since the P-value is greater than or equal to the level of significance α = 0.05, we reject the null hypothesis.

(v) Interpret the conclusion in the context of the application.