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

question 46

Multiple Choice

In constructing a confidence interval for $\sigma$ or $\sigma ^ { 2 }$ , a table is used to find the critical values $\chi _ { \mathrm { L } } ^ { 2 } \text { and } \chi _ { \mathrm { R } } ^ { 2 }$ for values of $n \leq 101$ For larger values of n, $\chi _ { \mathrm { L } } ^ { 2 } \text { and } \chi _ { \mathrm { R } } ^ { 2 }$ can be
approximated by using the following formula: $\chi ^ { 2 } = \frac { 1 } { 2 } \pm z _ { \alpha / 2 } + \sqrt { 2 k - 1 } ^ { 2 }$ where k is the number of degrees of freedom and $z _ { \alpha / 2 }$ is the critical 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 lb and a standard deviation of 25.5 lb. Round the confidence interval limits to the nearest hundredth.

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

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Definitions:

Self-Realization

The process of fully understanding and realizing one's own potential, abilities, and desires, often considered a goal in various psychological and spiritual traditions.

Self-Esteem

An individual's subjective evaluation of their own worth, embodying attitudes towards themselves ranging from positive to negative.

Trait Theories

Theories in psychology that focus on identifying, describing, and measuring individual differences in behavioral predispositions.

Self-Actualization

The act of reaching or fulfilling one's own capabilities and talents, perceived as an inherent desire or requirement in everyone.