Solve the problem.
-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 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

\chi _ { \mathrm { L } } ^ { 2 }

and

\chi _ { \mathrm { R } } ^ { 2 }

for a situation in which you wish to construct a

95 \%

confidence interval for

\sigma

and in which the sample size is

\mathrm { n } = 298

.
A)

\chi _ { \mathrm { L } } ^ { 2 } \approx 258.727 , \chi _ { \mathrm { R } } ^ { 2 } \approx 338.979

\chi _ { L } ^ { 2 } \approx 250.692 , \chi _ { R } ^ { 2 } \approx 346.150

\chi _ { \mathrm { L } } ^ { 2 } \approx 251.611 , \chi _ { \mathrm { R } } ^ { 2 } \approx 347.230

x _ { \mathrm { L } } ^ { 2 } \approx 257.795 , \chi _ { R } ^ { 2 } \approx 337.911

Solve the Problem. -Of 132 Adults Selected Randomly from One Town, 33 of Town

Multiple Choice