Solve the Problem $\sigma$ Or $\sigma ^ { 2 }$ , a Table Is Used to Find the Critical Values

question 69

Multiple Choice

Solve the problem.
-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 $\mathrm { n } \leq 101$ . For larger values of $\mathrm { n } , \chi _ { \mathrm { L } } ^ { 2 }$ and $\chi _ { \mathrm { R } } ^ { 2 }$ can be approximated by using the following formula:
$$\chi ^ { 2 } = \frac { 1 } { 2 } \left[ \pm z _ { \alpha / 2 } + \sqrt { 2 k - 1 } \right] ^ { 2 }$$
where $\mathrm { k }$ is the number of degrees of freedom and $\mathrm { z } \alpha / 2$ is the critical z score. Construct the $90 \%$ confidence interv: for $\sigma$ using the following sample data: a sample of size $n = 261$ yields a mean weight of $154 \mathrm { lb }$ and a standard deviation of $25.3 \mathrm { lb }$ . Round the confidence interval limits to the nearest hundredth.

• A) \(23.58 < \sigma < 27.24\)
• B) \(23.98 < \sigma < 26.83\)
• C) \(23.32 < \sigma < 27.71\)
• D) \(23.62 < \sigma < 27.30\)

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Definitions:

Store of Value

An asset that can be saved, retrieved, and exchanged at a later time without significant loss of value.

Money

A medium of exchange, a unit of account, and a store of value, used to facilitate transactions.

Wealth

An abundance of valuable resources or valuable material possessions, often measured in terms of assets like money, real estate, and personal property.

Bank Holding Company

A corporation that owns banks.