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:

Clayton Act

A U.S. antitrust law, adopted in 1914, aimed at protecting competition by prohibiting certain actions that lead to anticompetitiveness.

Celler-Kefauver Act

A U.S. law enacted in 1950 to amend the Clayton Act, aiming to prevent anti-competitive mergers and acquisitions by prohibiting the acquisition of assets if the effect reduces competition.

Mergers

The combination of two or more companies into one entity, often to enhance market share and reduce competition.

Celler-Kefauver Act

A U.S. law enacted in 1950, aimed at preventing anti-competitive mergers and acquisitions that could create monopolies or reduce competition.