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

\mathrm { n } \leq 101

. For larger values of

n , \chi _ { L } ^ { 2 }

and

\chi \frac { 2 } { \mathrm { 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. Estimate the critical values

x _ { L } ^ { 2 }

and

x _ { R } ^ { 2 }

for a situation in which you wish to construct a

95 \%

confidence interval for

\sigma

and in which the sample size is

n = 232

.
A)

\chi _ { L } ^ { 2 } \approx 190.338 , \chi _ { R } ^ { 2 } \approx 274.504

\chi _ { L } ^ { 2 } \approx 191.247 , \chi _ { R } ^ { 2 } \approx 275.595

\chi _ { L } ^ { 2 } \approx 196.533 , \chi _ { \mathrm { R } } ^ { 2 } \approx 267.173

\chi \underset { L } { 2 } \approx 197.457 , \chi \underset { R } { 2 } \approx 268.249

Use the Given Degree of Confidence and Sample Data to Construct

Multiple Choice