Specify the Appropriate Rejection Region for Testing $\mathrm { H } _ { 0 : } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$

question 94

Short Answer

Specify the appropriate rejection region for testing
$\mathrm { H } _ { 0 : } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ in the given situation.
- $\mathrm { H } _ { \mathrm { a } } : \sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 } ; \alpha = 0.10 , \mathrm { n } _ { 1 } = 10 , \mathrm { n } _ { 2 } = 16$
Assume that $s _ { 2 } ^ { 2 } > s _ { 1 } ^ { 2 }$ .
A) $F > 3.01$
B) $F > 2.59$
C) $| \mathrm { F } | > 2.34$
D) $| \mathrm { F } | > 2.59$ 9 Identify the rejection region that should be used to test $H _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ against $H _ { \mathrm { a } } : \sigma _ { 1 } ^ { 2 } \approx \sigma _ { 2 } ^ { 2 }$ for $v _ { 1 } = 5 , v _ { 2 } = 8$ , and $\alpha = .05$ .
A) $F > 4.82$
B) $F > 3.69$
C) $F > 6.76$
D) $F > 6.63$ 10 Identify the rejection region that should be used to test $H _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }$ against $H _ { a } : \sigma _ { 1 } { } ^ { 2 } > \sigma _ { 2 } ^ { 2 }$ for $v _ { 1 } = 10$ , v $v _ { 2 } = 29$ , and $\alpha = .10$ .
A) $F > 1.83$
B) $F > 2.18$
C) $F > 2.53$
D) $F > 3.00$

• A) \(F > 3.01\)
• B) \(F > 2.59\)
• C) \(| \mathrm { F } | > 2.34\)
• D) \(| \mathrm { F } | > 2.59\) 9 Identify the rejection region that should be used to test \(H _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }\) against \(H _ { \mathrm { a } } : \sigma _ { 1 } ^ { 2 } \approx \sigma _ { 2 } ^ { 2 }\) for \(v _ { 1 } = 5 , v _ { 2 } = 8\), and \(\alpha = .05\).
• A) \(F > 4.82\)
• B) \(F > 3.69\)
• C) \(F > 6.76\)
• D) \(F > 6.63\) 10 Identify the rejection region that should be used to test \(H _ { 0 } : \sigma _ { 1 } ^ { 2 } = \sigma _ { 2 } ^ { 2 }\) against \(H _ { a } : \sigma _ { 1 } { } ^ { 2 } > \sigma _ { 2 } ^ { 2 }\) for \(v _ { 1 } = 10\), v \(v _ { 2 } = 29\), and \(\alpha = .10\).
• A) \(F > 1.83\)
• B) \(F > 2.18\)
• C) \(F > 2.53\)
• D) \(F > 3.00\)

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Definitions:

Plantwide Factory Overhead Rate

A single overhead absorption rate calculated by dividing total factory overheads by total machine hours or labor hours, applied uniformly across all products and services.

Machine Hours

A measure of the amount of time a machine is operated, used in costing and operational efficiency analysis.

Single Plantwide Factory Overhead Rate

A method of allocating manufacturing overhead costs uniformly across all units produced within a single factory.

Direct Labor Hours

The total hours worked by employees who are directly involved in the production of goods or services.