In Constructing a Confidence Interval For $\sigma$ Or $\sigma ^ { 2 }$

question 110

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 $\chi \underset { R } { 2 }$ for values of $n \leq 101$ . For larger values of $n , \chi _ { L } ^ { 2 }$ and $\chi { } _ { \mathrm { R } } ^ { 2 }$ can be approximated by using the following formula: $\chi ^ { 2 } = \frac { 1 } { 2 } [ \pm \mathrm { z } \alpha / 2 + \sqrt { 2 \mathrm { k } - 1 } ] ^ { 2 }$ where $\mathrm { k }$ is the number of degrees of freedom and $\mathrm { z } \alpha / 2$ is the critical z score. Construct the $90 \%$ confidence interval for $\sigma$ using the following sample data: a sample of size $\mathrm { n } = 234$ yields a mean weight of $155 \mathrm { lb }$ and a standard deviation of $26.0 \mathrm { lb }$ . Round the confidence interval limits to the nearest hundredth.

• A) \(24.13 \mathrm { lb } < \sigma < 28.11 \mathrm { lb }\)
• B) \(24.18 \mathrm { lb } < \sigma < 28.18 \mathrm { lb }\)
• C) \(24.57 \mathrm { lb } < \sigma < 27.67 \mathrm { lb }\)
• D) \(23.86 \mathrm { lb } < \sigma < 28.63 \mathrm { lb }\)

Understand how physical activities and dietary choices influence metabolism and weight management.

Explain the impact of emotional states and cognitive appraisals on physical sensations and responses.

Recognize the brain structures involved in emotional experiences, intuition, and emotional regulation.

Understand theories of emotion and their implications for interpreting and experiencing emotions.

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Definitions:

Groupthink

A phenomenon where the desire for group consensus and cohesiveness leads to poor decision-making processes and outcomes.

Maintaining Harmony

The act of keeping relationships or environments peaceful and cooperative.

Critically Thinking

The process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and evaluating information to reach an answer or conclusion.

Storming Stage

A phase in group development characterized by conflict and competition as members assert their opinions and vie for positions within the group.