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In Constructing a Confidence Interval For σ\sigma Or σ2\sigma ^ { 2 }

question 46

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In constructing a confidence interval for σ\sigma or σ2\sigma ^ { 2 } , a table is used to find the critical values χL2 and χR2\chi _ { \mathrm { L } } ^ { 2 } \text { and } \chi _ { \mathrm { R } } ^ { 2 } for values of n101n \leq 101 For larger values of n, χL2 and χR2\chi _ { \mathrm { L } } ^ { 2 } \text { and } \chi _ { \mathrm { R } } ^ { 2 } can be
approximated by using the following formula: χ2=12±zα/2+2k12\chi ^ { 2 } = \frac { 1 } { 2 } \pm z _ { \alpha / 2 } + \sqrt { 2 k - 1 } ^ { 2 } where k is the number of degrees of freedom and zα/2z _ { \alpha / 2 } is the critical z-score. Construct the 90 % confidence interval for σ\sigma using the following sample data: a sample of size n=232 yields a mean weight of 154 lb and a standard deviation of 25.5 lb. Round the confidence interval limits to the nearest hundredth.

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Definitions:

Noncustodial Fathers

Fathers who do not have legal custody of their child/children, and thus the children reside primarily with the other parent.

Custodial Mother

A mother who has been granted primary legal and/or physical custody of her child(ren) by a court.

Child Support

Financial contributions required by law to be made by a non-custodial parent to support their child(ren)'s upbringing and welfare.

Remarriage

Entering into marriage again after one or more previous marriages have ended through divorce or widowhood.

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