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 σ2 or σ, 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 σ2 or σ
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: σ12 = σ22; H1: σ12 > σ22
b.H0: σ12 < σ22; H1: σ12 = σ22
c.H0: σ12 = σ22; H1: σ12 < σ22
d.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.
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 α = 0.05, we fail to reject the null hypothesis.
b.Since the P-value is less than the level of significance α = 0.05, we reject the null hypothesis.
c.Since the P-value is less than the level of significance α = 0.05, we fail to reject the null hypothesis.
d.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.
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.

Looking for a Similar Assignment? Order now and Get 10% Discount! Use Coupon Code "Newclient"