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

question 46

Multiple Choice

In constructing a confidence interval for $\sigma$ or $\sigma ^ { 2 }$ , a table is used to find the critical values $\chi _ { \mathrm { L } } ^ { 2 } \text { and } \chi _ { \mathrm { R } } ^ { 2 }$ for values of $n \leq 101$ For larger values of n, $\chi _ { \mathrm { L } } ^ { 2 } \text { and } \chi _ { \mathrm { R } } ^ { 2 }$ can be
approximated by using the following formula: $\chi ^ { 2 } = \frac { 1 } { 2 } \pm z _ { \alpha / 2 } + \sqrt { 2 k - 1 } ^ { 2 }$ where k is the number of degrees of freedom and $z _ { \alpha / 2 }$ is the critical z-score. Construct the 90 % confidence interval for $\sigma$ 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.

• A) \(23.66 \mathrm { lb } < \sigma < 27.58 \mathrm { lb }\)
• B) \(23.39 \mathrm { lb } < \sigma < 28.09 \mathrm { lb }\)
• C) \(24.09 \mathrm { lb } < \sigma < 27.15 \mathrm { lb }\)
• D) \(23.71 \mathrm { lb } < \sigma < 27.65 \mathrm { lb }\)

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Definitions:

Marginal Analysis

An economic approach that involves comparing the additional benefits of an activity to its additional costs.

Marginal Analysis

Marginal analysis is the examination of the benefits and costs of an incremental change in the production or consumption of goods or services.

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Marginal Analysis

Marginal Analysis is an assessment method used to evaluate the impact of a small change in production levels or economic activity, focusing on the cost and benefit of making that change.