Two processes for manufacturing large roller bearings are under study. In both cases, the diameters (in centimeters) are being examined. A random sample of26roller bearings from the old manufacturing process showed the sample variance of diameters to bes²=0.25.

Another random sample of29roller bearings from the new manufacturing process showed the sample variance of their diameters to bes²=0.125.

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 estimating²or,Ftest for two variances, One-way ANOVA, or Two-way ANOVA, then perform the following.

Chi-square goodness-of-fit

Ftest for two variances

Two-way ANOVA

One-way ANOVA

Chi-square for testing or estimating²or

Chi-square test of homogeneity

Chi-square test of independence

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

State the null and alternate hypotheses.

H₀:₁²=₂²;H₁:₁²<₂²

H₀:₁²<₂²;H₁:₁²=₂²

H₀:₁²=₂²;H₁:₁²₂²

H₀:₁²=₂²;H₁:₁²>₂²

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

(iii) Find theP-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 theP-value is greater than or equal to the level of significance= 0.05, we fail to reject the null hypothesis.

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

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

Since theP-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.

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

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

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

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