Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in centimeters) are being examined. A random sample of 26 roller bearings from the old manufacturing process showed the sample variance of diameters to be

s2 = 0.214.

Another random sample of 29 roller bearings from the new manufacturing process showed the sample variance of their diameters to be

s2 = 0.121.

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 estimating 2 or , F test for two variances, One-way ANOVA, or Two-way ANOVA, then perform the following.

a.One-way ANOVA

b.Chi-square goodness-of-fit

c.Chi-square test of independence

d.Chi-square for testing or estimating 2 or

e.Chi-square test of homogeneity

f.Two-way ANOVA

g.F test for two variances

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

State the null and alternate hypotheses.

a.H0: 12 = 22; H1: 12 > 22

b.H0: 12 < 22; H1: 12 = 22

c.H0: 12 = 22; H1: 12 < 22

d.H0: 12 = 22; H1: 12 22

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

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

a.P-value > 0.200

b.0.100 < P-value < 0.200

c.0.050 < P-value < 0.100

d.0.020 < P-value < 0.050

e.0.002 < P-value < 0.020

f.P-value < 0.002

(iv) Conclude the test.

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

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

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

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

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

a.At the 5% level of significance, there is insufficient evidence to show that the variance for the new manufacturing process is different.

b.At the 5% level of significance, there is sufficient evidence to show that the variance for the new manufacturing process is not different.

c.At the 5% level of significance, there is insufficient evidence to show that the variance for the new manufacturing process is not different.

d.At the 5% level of significance, there is sufficient evidence to show that the variance for the new manufacturing process is different.