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

question 25

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 $\mathrm { n } \leq 101$ . For larger values of $n , \chi _ { L } ^ { 2 }$ and $\chi \frac { 2 } { \mathrm { R } }$ 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. Estimate the critical values $x _ { L } ^ { 2 }$ and $x _ { R } ^ { 2 }$ for a situation in which you wish to construct a $95 \%$ confidence interval for $\sigma$ and in which the sample size is $n = 232$ .

• A) \(\chi _ { L } ^ { 2 } \approx 190.338 , \chi _ { R } ^ { 2 } \approx 274.504\)
• B) \(\chi _ { L } ^ { 2 } \approx 191.247 , \chi _ { R } ^ { 2 } \approx 275.595\)
• C) \(\chi _ { L } ^ { 2 } \approx 196.533 , \chi _ { \mathrm { R } } ^ { 2 } \approx 267.173\)
• D) \(\chi \underset { L } { 2 } \approx 197.457 , \chi \underset { R } { 2 } \approx 268.249\)

---

Definitions:

Frequency

In the context of waves, it is the number of waves that pass a fixed point per second; in general use, it refers to how often something occurs.

Intensity

The degree of strength, force, energy, or feeling in a given situation, often used in various physical and emotional contexts.

Sound Waves

Sounds that move through air or different mediums and become audible when they arrive at an individual's or animal's ear.

Greater-Amplitude

Pertains to signals or waves with higher magnitude or intensity, often used in the context of physical or biological measurements.