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? −40, 78, −24, −70, −42, 10, 15, 52, −7, −51, −106, −106 . . . Question content area right Part 1 What are the null and alternative hypotheses? A. H0: σ=32.2 ft H1: σ>32.2 ft B. H0: σ<32.2 ft H1: σ=32.2 ft C. H0: σ=32.2 ft H1: σ<32.2 ft D. H0: σ≠32.2 ft H1: σ=32.2 ft E. H0: σ>32.2 ft H1: σ=32.2 ft F. H0: σ=32.2 ft H1: σ≠32.2 ft Part 2 Find the test statistic. χ2=enter your response here (Round to two decimal places as needed.) Part 3 Determine the critical value(s). The critical value(s) is/are enter your response here. (Use a comma to separate answers as needed. Round to two decimal places as needed.) Part 4 Since the test statistic is ▼ between less than equal to greater than the critical value(s), ▼ rejectreject fail to rejectfail to reject H0. There is ▼ insufficient sufficient evidence to support the claim that the new production method has errors with a standard deviation greater than 32.2 ft. Part 5 The variation appears to be ▼ about the same greater less than in the past, so the new method appears to be ▼ similar better worse , 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.
Test the given claim. Assume that a simple random sample is selected from a
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?
−40, 78, −24, −70, −42, 10, 15, 52, −7, −51, −106, −106
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Question content area right
Part 1
What are the null and alternative hypotheses?
A.
H0: σ=32.2 ft
H1: σ>32.2 ft
B.
H0: σ<32.2 ft
H1: σ=32.2 ft
C.
H0: σ=32.2 ft
H1: σ<32.2 ft
D.
H0: σ≠32.2 ft
H1: σ=32.2 ft
E.
H0: σ>32.2 ft
H1: σ=32.2 ft
F.
H0: σ=32.2 ft
H1: σ≠32.2 ft
Part 2
Find the test statistic.
χ2=enter your response here
(Round to two decimal places as needed.)
Part 3
Determine the critical value(s).
The critical value(s) is/are enter your response here.
(Use a comma to separate answers as needed. Round to two decimal places as needed.)
Part 4
Since the test statistic is
▼
between
less than
equal to
greater than
the critical value(s),
▼
rejectreject
fail to rejectfail to reject
H0. There is
▼
insufficient
sufficient
evidence to support the claim that the new production method has errors with a standard deviation greater than 32.2 ft.
Part 5
The variation appears to be
▼
about the same
greater
less
than in the past, so the new method appears to be
▼
similar
better
worse
, 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.
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