Provide an Appropriate Response $\sigma$ Or $\sigma ^ { 2 }$ , a Table Is Used to Find the Critical Values

question 25

Multiple Choice

Provide an appropriate response.
-In constructing a confidence interval for $\sigma$ or $\sigma ^ { 2 }$ , a table is used to find the critical values $\chi _ { L } ^ { 2 }$ and $\chi _ { R } ^ { 2 }$ for values of $\mathrm { n } \leq 101$ . For larger values of $n , \chi _ { L } ^ { 2 }$ and $\chi \frac { 2 } { \mathrm { R } }$ can be approximated by using the following formula: $\chi ^ { 2 } =$ $\frac { 1 } { 2 } \left[ \pm \mathrm { z } _ { \alpha / 2 } + \sqrt { 2 \mathrm { k } - 1 } \right] ^ { 2 }$ where $\mathrm { k }$ is the number of degrees of freedom and $\mathrm { z } _ { \alpha / 2 }$ is the critical $\mathrm { z }$ score. Estimate the critical values $x _ { L } ^ { 2 }$ and $x _ { R } ^ { 2 }$ for a situation in which you wish to construct a $95 \%$ confidence interval for $\sigma$ and in which the sample size is $n = 232$ .

• A) \(\chi _ { L } ^ { 2 } \approx 190.338 , \chi _ { R } ^ { 2 } \approx 274.504\)
• B) \(\chi _ { L } ^ { 2 } \approx 191.247 , \chi _ { R } ^ { 2 } \approx 275.595\)
• C) \(\chi _ { L } ^ { 2 } \approx 196.533 , \chi _ { \mathrm { R } } ^ { 2 } \approx 267.173\)
• D) \(\chi \underset { L } { 2 } \approx 197.457 , \chi \underset { R } { 2 } \approx 268.249\)

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Definitions:

High-High Style

A leadership approach emphasizing high levels of both task orientation and relationship orientation in managing teams or organizations.

Performance Outcomes

The results or achievements derived from the efforts and actions of an individual or team in a given task or objective.

Behavioral Approach

A perspective in leadership and psychology that emphasizes observable actions and responses, rather than internal mental states.

High-High Style

A leadership approach that is high in both task orientation and relationship orientation, balancing work requirements with support for team members.