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Solve the Problem σ\sigma Or σ2\sigma ^ { 2 } , a Table Is Used to Find the Critical Values

question 62

Multiple Choice

Solve the problem.
-In constructing a confidence interval for σ\sigma or σ2\sigma ^ { 2 } , a table is used to find the critical values χL2\chi _ { L } ^ { 2 } and χR2\chi _ { R } ^ { 2 } for values
of n101n \leq 101 . For larger values of n,χL2n , \chi _ { L } ^ { 2 } and χ2R\chi \frac { 2 } { R } can be approximated by using the following formula:
χ2=12[±zα/2+2k1]2\chi ^ { 2 } = \frac { 1 } { 2 } \left[ \pm z _ { \alpha / 2 } + \sqrt { 2 \mathrm { k } - 1 } \right] ^ { 2 }
where k\mathrm { k } is the number of degrees of freedom and zα/2\mathrm { z } _ { \alpha / 2 } is the critical z\mathrm { z } score. Estimate the critical values χL2\chi _ { \mathrm { L } } ^ { 2 } and χR2\chi _ { \mathrm { R } } ^ { 2 } for a situation in which you wish to construct a 95%95 \% confidence interval for σ\sigma and in which the sample size is n=298\mathrm { n } = 298 .


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