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Compare the Sampling Distributions of the Normally Distributed Test Statistic

question 24

Essay

Compare the sampling distributions of the normally distributed test statistic z and the chi-square test statistic. Specifically, how do the sampling distributions differ in shape and range of values?

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Definitions:

Goodness-of-Fit Test

A statistical test used to compare an observed distribution to an expected distribution, to check how well the observed data fits with a specific distribution.

Probability Distribution

A mathematical description that assigns probabilities to different outcomes of a random variable.

Chi-Square Distribution

The Chi-Square Distribution is a statistical distribution used for hypothesis testing and is derived from the sum of the squares of a set of normally distributed random variables.

Degrees of Freedom

The number of values in the final calculation of a statistic that are free to vary.

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