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?

negative 44−44​,

7777​,

negative 24−24​,

negative 75−75​,

negative 45−45​,

1212​,

1616​,

5353​,

negative 7−7​,

negative 54−54​,

negative 107−107​,

negative 107−107  

What are the null and alternative​ hypotheses?

A.

H0​:

sigmaσless than<32.2

ft

H1​:

sigmaσequals=32.2

ft

B.

H0​:

sigmaσequals=32.2

ft

H1​:

sigmaσgreater than>32.2

ft

C.

H0​:

sigmaσequals=32.2

ft

H1​:

sigmaσless than<32.2

ft

D.

H0​:

sigmaσgreater than>32.2

ft

H1​:

sigmaσequals=32.2

ft

E.

H0​:

sigmaσequals=32.2

ft

H1​:

sigmaσnot equals≠32.2

ft

F.

H0​:

sigmaσnot equals≠32.2

ft

H1​:

sigmaσequals=32.2

ft

Find the test statistic.

chi squaredχ2equals=nothing

​(Round to two decimal places as​ needed.)

Determine the critical​ value(s).

The critical​ value(s) is/are

nothing.

​(Use a comma to separate answers as needed. Round to two decimal places as​ needed.)

Since the test statistic is

▼

equal to

greater than

between

less than

the critical​ value(s),

▼

fail to rejectfail to reject

rejectreject

Upper H 0H0.

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.

Answer 1