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

question 110

Multiple Choice

In constructing a confidence interval for $\sigma$ or $\sigma ^ { 2 }$ , a table is used to find the critical values $\chi _ { L } ^ { 2 }$ and $\chi \underset { R } { 2 }$ for values of $n \leq 101$ . For larger values of $n , \chi _ { L } ^ { 2 }$ and $\chi { } _ { \mathrm { R } } ^ { 2 }$ can be approximated by using the following formula: $\chi ^ { 2 } = \frac { 1 } { 2 } [ \pm \mathrm { z } \alpha / 2 + \sqrt { 2 \mathrm { k } - 1 } ] ^ { 2 }$ where $\mathrm { k }$ is the number of degrees of freedom and $\mathrm { z } \alpha / 2$ is the critical z score. Construct the $90 \%$ confidence interval for $\sigma$ using the following sample data: a sample of size $\mathrm { n } = 234$ yields a mean weight of $155 \mathrm { lb }$ and a standard deviation of $26.0 \mathrm { lb }$ . Round the confidence interval limits to the nearest hundredth.

• A) \(24.13 \mathrm { lb } < \sigma < 28.11 \mathrm { lb }\)
• B) \(24.18 \mathrm { lb } < \sigma < 28.18 \mathrm { lb }\)
• C) \(24.57 \mathrm { lb } < \sigma < 27.67 \mathrm { lb }\)
• D) \(23.86 \mathrm { lb } < \sigma < 28.63 \mathrm { lb }\)

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