Provide an Appropriate Response $\sigma$ Or $\sigma ^ { 2 }$ , a Table Is Used to Find the Critical Values

question 104

Multiple Choice

Provide an appropriate response.
-In constructing a confidence interval for $\sigma$ or $\sigma ^ { 2 }$ , a table is used to find the critical values $\chi { } _ { L } ^ { 2 }$ and $\chi { } _ { R } ^ { 2 }$ for values of $n \leq 101$ . For larger values of $n , \chi { } _ { L } ^ { 2 }$ and $\chi \frac { 2 } { R }$ 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 $\mathrm { z }$ score. Construct the $90 \%$ confidence interval for $\sigma$ using the following sample data: a sample of size $n = 232$ yields a mean weight of $154 \mathrm { lb }$ and a standard deviation of $25.5 \mathrm { lb }$ . Round the confidence interval limits to the nearest hundredth.

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

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Definitions:

Equilibrium Price

The price at which the quantity of goods supplied is equal to the quantity of goods demanded, also known as the market-clearing price.

Demand Curve

A diagram illustrating how the price of a product correlates with the amount of that product buyers are prepared and can afford to buy at different price levels.

Inverse Relationship

A situation in which two variables move in opposite directions, meaning that as one variable increases, the other decreases, and vice versa.

Quantity Rises

An increase in the amount or number of a particular good or service that is available or produced.