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) \(\chi _ { \mathrm { L } } ^ { 2 } \approx 254.998 , \chi _ { \mathrm { R } } ^ { 2 } \approx 334.708\)

Identify and explain the structural and functional aspects of hydrostatic skeletons and coelomates.

Identify and apply the rules for naming branched alkanes and their isomers.

Understand and describe the condensed structural formula representation of hydrocarbons.

Recognize and name cyclic alkanes and their general molecular formulas.

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Definitions:

Contact Metamorphism

A type of metamorphism that occurs when rocks are heated by the intrusion of hot magma without melting.

Subduction

The process whereby one tectonic plate moves under another plate and is forced to sink into the mantle, often leading to volcanic activity and earthquakes.

Normal Faulting

A type of faulting where the crust is extended and the hanging wall moves down relative to the footwall.

Partly Metamorphic

Relating to rocks that have been partially altered in structure or composition by heat, pressure, or chemical processes.