Book cover for Statistics

Statistics

Barbara Illowsky, Susan Dean

ISBN #9781951693220

1st Edition

1,473 Questions

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Homework Questions

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Summary

Learning Objectives

Key Concepts

Example Problems

Explanations

Common Mistakes

Summary

The chapter on the chi-square distribution introduces various chi-square tests used in hypothesis testing for categorical data. Key topics include identifying when to use the goodness-of-fit test versus tests of independence and homogeneity, calculating the chi-square statistic using observed and expected frequencies, and determining degrees of freedom based on the structure of your data. Most chi-square tests are right-tailed, meaning that larger test statistic values indicate a greater discrepancy between observed and expected values, leading to rejection of the null hypothesis if the p-value is sufficiently small.

Learning Objectives

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Key Concepts

CONCEPT

DEFINITION

Confidence Intervals

A range of plausible values for a population parameter, computed from sample data. It incorporates the sample mean, the margin of error (based on a z-score when the population standard deviation is known), and the standard error (?/?n) to express uncertainty in estimates.

Example Problems

Example 1

If the number of degrees of freedom for a chi-square distribution is $25,$ what is the population mean and standard deviation?

Example 2

If $d f>90,$ the distribution is ________ If $d f=15,$ the distribution is ________.

Example 3

When does the chi-square curve approximate a normal distribution?

Example 4

Where is $\mu$ located on a chi-square curve?

Example 5

Is it more likely the $d f$ is $90,20,$ or 2 in the graph?

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Step-by-Step Explanations

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Common Mistakes

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