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

question 29

Multiple Choice

In constructing a confidence interval for $\sigma$ or $\sigma ^ { 2 }$ , 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) \(\chi _ { L } ^ { 2 } \approx 255.930 , \chi _ { R } ^ { 2 } \approx 335.776\)
• B) \(\chi _ { \mathrm { L } } ^ { 2 } \approx 247.934 , \chi _ { \mathrm { R } } ^ { 2 } \approx 342.908\)
• C) \(\chi _ { L } ^ { 2 } \approx 248.853 , \chi _ { R } ^ { 2 } \approx 343.989\)
• D) \(\chi _ { \mathrm { L } } ^ { 2 } \approx 254.998 , \chi _ { \mathrm { R } } ^ { 2 } \approx 334.708\)

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Definitions:

Inventory Holding Costs

encompass all expenses related to storing unsold goods, including warehousing, insurance, depreciation, opportunity cost, and spoilage, significant in inventory management decisions.

Pilferage

The theft of small quantities of goods, typically from an employer or a retail setting, often considered a form of inventory shrinkage.

Scrap

Material that is discarded or deemed as waste during the manufacturing process, often due to defects, excess, or irrelevance to the final product.

Obsolescence

The process of becoming outdated or no longer used, often because of the introduction of newer and more effective technologies or products.