In Constructing a Confidence Interval For $\sigma$ Or $\sigma ^ { 2 }$

question 13

Multiple Choice

In constructing a confidence interval for $\sigma$ or $\sigma ^ { 2 }$ , a table is used to find the critical values $\chi _ { \mathrm { L } } ^ { 2 }$ and $\chi _ { \mathrm { R } } ^ { 2 }$ for values of $n \leq 101$ . For larger values of $n , \chi _ { \mathrm { L } } ^ { 2 }$ and $\chi _ { \mathrm { R } } ^ { 2 }$ can be approximated by using the following formula: $\chi ^ { 2 } = \frac { 1 } { 2 } \pm z _ { \alpha / 2 } + \sqrt { 2 k - 1 } ^ { 2 }$ where $k$ is the number of degrees of freedom and $z _ { \alpha / 2 }$ is the critical $z$ -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) \(23.66 \mathrm { lb } < \sigma < 27.58 \mathrm { lb }\)
• B) \(23.39 \mathrm { lb } < \sigma < 28.09 \mathrm { lb }\)
• C) \(24.09 \mathrm { lb } < \sigma < 27.15 \mathrm { lb }\)
• D) \(23.71 \mathrm { lb } < \sigma < 27.65 \mathrm { lb }\)

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Definitions:

Planning

The process of setting goals, developing strategies, and outlining tasks and schedules to achieve the goals.

Product/Service Quality

The measure of excellence or state of being free from defects, deficiencies, and significant variations, assessed by comparing a product or service to established standards.

Mary Parker Follett

A pioneering theorist in organizational behavior and management who emphasized the importance of integrative conflict resolution and human relations.

Build-It-In Approach

A methodology focusing on integrating quality and efficiency into the process of product or service development rather than inspecting quality after production.