The Test Statistic Employed to Test $H _ { 0 } : \sigma _ { 1 } ^ { 2 } / \sigma _ { 2 } ^ { 2 } = 1$

question 36

True/False

The test statistic employed to test $H _ { 0 } : \sigma _ { 1 } ^ { 2 } / \sigma _ { 2 } ^ { 2 } = 1$ is $F = s _ { 1 } ^ { 2 } / s _ { 2 } ^ { 2 }$
, which is F-distributed with $v _ { 1 } = n _ { 1 } - 1 \text { and } v _ { 2 } = n _ { 2 } - 1$ degrees of freedom, provided that the two populations are F-distributed.

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Definitions:

Random Assignment

A method used in experiments to place participants into different groups in a way that each person has an equal chance of being in any group, minimizing biases and ensuring the groups are comparable at the start.

Cause and Effect

A relationship between events or things, where one is the result of the other or others; a principle of causality.

Random Assignment

The process of assigning study participants to different groups using randomization, to ensure that every participant has an equal chance of being assigned to any given group.

Random Sampling

A method used in statistical sampling where each member of a population has an equal chance of being included in the sample, enhancing the representativeness of the results.