In constructing a confidence interval for

\sigma

\sigma ^ { 2 }

, a table is used to find the critical values

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

and

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

for values of

\mathrm { 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 } \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 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

n = 295

.
A)

\chi _ { L } ^ { 2 } \approx 255.930 , \chi _ { R } ^ { 2 } \approx 335.776

\chi _ { \mathrm { L } } ^ { 2 } \approx 247.934 , \chi _ { \mathrm { R } } ^ { 2 } \approx 342.908

\chi _ { L } ^ { 2 } \approx 248.853 , \chi _ { R } ^ { 2 } \approx 343.989

\chi _ { \mathrm { L } } ^ { 2 } \approx 254.998 , \chi _ { \mathrm { R } } ^ { 2 } \approx 334.708

Assume That a Sample Is Used to Estimate a Population n=6400,x=1920\mathrm { n } = 6400 , \mathrm { x } = 1920n=6400,x=1920

Multiple Choice