Question

1. Ball bearings used in commercial airlines can only tolerate a maximum variance without increasing the risk of crashes. The industry requirement places the upper limit for this safety boundary at 0.0009 in standard units. A new batch of 30 ball bearings from a new supplier has a sample variance = 0.0010. The acceptable level of alpha here is 0.05.

Which test would you use a Chi-Square or an F- test and why? Would this be a one-tailed test or a two-tailed test for variance? You don’t have to answer these questions here. Do it in the Hypothesis test set-up.

Test the hypothesis that the sample variance of new batch would be meet the industry’s standards against the alternative that the new batch is outside the acceptable limit. US alpha = .05 for a test of variance.

Set up the four steps properly.

1. State the Two Hypotheses

2. Determine the Critical Rejection value(s)

3. Calculate the test statistic

4. State the conclusion and its implications to the airline ball bearing purchasers.

Answer 1

This is a test on one variance we perform chi square test.

Hypothesis:

H0: <=  0.0009

H1: > 0.0009

degrees of freedom = 30 -1 = 29

critical value = = = 42.56

If chi square is greater than critical value reject H0.

test statistic = (29*0.001)/0.0009 = 32.22

Since < we fail to reject H0 and there is no significant evidence that variance is more than 0.0009. these ball bearings can tolerate.