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

question 104

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 $n \leq 101$ . For larger values of $n , \chi { } _ { L } ^ { 2 }$ and $\chi \frac { 2 } { R }$ 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. Construct the $90 \%$ confidence interval for $\sigma$ using the following sample data: a sample of size $n = 232$ yields a mean weight of $154 \mathrm { lb }$ and a standard deviation of $25.5 \mathrm { lb }$ . Round the confidence interval limits to the nearest hundredth.

• A) \(23.71 \mathrm { lb } < \sigma < 27.65 \mathrm { lb }\)
• B) \(23.66 \mathrm { lb } < \sigma < 27.58 \mathrm { lb }\)
• C) \(23.39 \mathrm { lb } < \sigma < 28.09 \mathrm { lb }\)
• D) \(24.09 \mathrm { lb } < \sigma < 27.15 \mathrm { lb }\)

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Definitions:

Creative Destruction

The replacement of existing products, processes, ideas, and businesses with new and better ones.

Economies of Scale

The economic benefits that companies gain from their size of operation, whereby the expense per output unit typically diminishes as the scale expands.

Large Quantities

A significant amount or number of items or material, often related to production or purchasing operations.

Valuable Asset

An item, thing, or entity that is of great worth or importance in achieving goals or in the financial standing of an organization or individual.