In a Hypothesis Test for the Population Variance, the Hypotheses $$H _ { 0 } : \sigma ^ { 2 } = 175$$

question 63

Short Answer

In a hypothesis test for the population variance, the hypotheses are: $$H _ { 0 } : \sigma ^ { 2 } = 175$$ $$\Pi _ { 1 } : \sigma ^ { 2 } \neq 175$$ If the sample size is 25 and the test is being carried out at the 5% level of significance, the rejection region will be: $\begin{array}{|l|l|}\hline A&\chi^{2}<15.6587 \text { or } \chi^{2}>33.1963 .\\\hline B&\chi^{2}<12.4011 \text { or } \chi^{2}>39.3641\\\hline C&\chi^{2}<16.4734 \text { or } \chi^{2}>34.3816\\\hline D&\chi^{2}<13.1197 \text { or } \chi^{2}<37.6525 .\\\hline\end{array}$

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Definitions:

Significant Differences

A term used in statistics to indicate that the differences observed between groups or variables are unlikely to have occurred by chance.

Generalize Findings

The process of applying the results of a study or conclusion beyond the specific contexts or participants studied.

Descriptive Statistics

Statistical methods that summarize or describe a collection of data using measures such as mean, median, and mode.

Population Parameters

Quantitative characteristics or metrics of a population, such as mean, variance, or standard deviation.