Question

Test the given claim. Assume that a simple random sample is selected from a normally distributed population. Use either the​ P-value method or the traditional method of testing hypotheses.

Company A uses a new production method to manufacture aircraft altimeters. A simple random sample of new altimeters resulted in errors listed below. Use a 0.05 level of significance to test the claim that the new production method has errors with a standard deviation greater than 32.2​ ft, which was the standard deviation for the old production method. If it appears that the standard deviation is​ greater, does the new production method appear to be better or worse than the old​ method? Should the company take any​ action?

−45​,78​,−24​,−71​,−42​,13​,19​,53​,−8​,−54​,−106​,−106

Find the test statistic

χ2=

Determine the critical​ value(s).

The critical​ value(s) is/are

Since the test statistic is

(greater than, less than, between, equal to)

the critical​ value(s), (reject, fail to reject) H0.

There is(sufficient, insufficient) evidence to support the claim that the new production method has errors with a standard deviation greater than 32.2 ft.

The variation appears to be (greater, about the same, less, greater) than in the​ past, so the new method appears to be (worse, better, similar) because there will be (more, fewer, the same number) of altimeters that have errors.​ Therefore, the company(should, should not) take immediate action to reduce the variation.

Answer 1