Test the given claim. Assume that a simple random sample isselected 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 aircraftaltimeters. A simple random sample of new altimeters resulted inerrors listed below. Use a 0.05 level of significance to test theclaim that the new production method has errors with a standarddeviation greater than 32.2​ ft, which was the standard deviationfor the old production method. If it appears that the standarddeviation is​ greater, does the new production method appear to bebetter 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 claimthat the new production method has errors with a standard deviationgreater 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 samenumber) of altimeters that have errors.​ Therefore, thecompany(should, should not) take immediate action to reduce thevariation.