Question

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 = 0.221.

Another random sample of 26 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.

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

Answer 1

The null and alternative hypothesis is ,

The sample test statistic is ,

The critical values are ,

; The Excel function is , =FINV(0.025,25,25)

; ; The Excel function is , =FINV(0.975,25,25)

Decision : Here , the value of the test statistic lies in the rejction region.

Therefore , reject the null hypothesis.

Conclusion : Hence , there is sufficient evidence to support the claim that there is a difference (either way) in the population variances between the old and new manufacturing processes.