Provide an appropriate response.
-In constructing a confidence interval for

\sigma

\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 }

23.66 \mathrm { lb } < \sigma < 27.58 \mathrm { lb }

23.39 \mathrm { lb } < \sigma < 28.09 \mathrm { lb }

24.09 \mathrm { lb } < \sigma < 27.15 \mathrm { lb }

Assume That a Sample Is Used to Estimate a Population

Multiple Choice