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:

Individual Demand Curve

A graphical representation showing the quantity of a goods or services a single consumer is willing and able to purchase at various prices.

Budget Constraints

The limitations on the spending behavior of consumers, based on their income and the prices of goods and services.

Indifference Curves

Representations on a graph showing combinations of goods or services between which a consumer is indifferent, meaning they have no preference for one combination over another.

Elasticity

Elasticity refers to the degree to which demand or supply reacts to changes in price or other factors.