Statistical Inferences Using the Chi-Square Distribution

Previously, we looked at confidence intervals and hypothesis tests involving population means and population proportions, both single-population and two-populations scenarios. But what about other population parameters, such as the population variance? Like the other population parameters, we want to construct a confidence interval or conduct a hypothesis test for a single population variance. Unlike the population mean or the population variance, which use the normal or [latex]t[/latex]-distributions, to study the population variance, we need to use a new distribution called the [latex]\chi^2[/latex]-distribution.

Other situations use the [latex]\chi^2[/latex]-distribution. For example, have you ever wondered if lottery numbers were evenly distributed or if some numbers occurred with a greater frequency?  How about if the types of movies people preferred were different across different age groups? What about whether a coffee machine was dispensing approximately the same amount of coffee each time? These situations involve testing how well an observed distribution of data fits the expected distribution. These types of scenarios require a hypothesis test using the [latex]\chi^2[/latex]-distribution.

“10.1 Introduction to Statistical Inferences Using the Chi-Square Distribution” from Introduction to Statistics by Valerie Watts is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.