Advanced Hypothesis Testing

Chi-Square Goodness of Fit Test

1. Hypothesis Testing

Hypothesis testing is a fundamental tool in statistics that helps us make inferences about populations based on samples. It is used to evaluate the plausibility of a claim, or hypothesis, about a population parameter using sample data.
In this tutorial, we will cover some of the more advanced techniques used in hypothesis testing.

TODO - Before coming to probem statement,

• PRE REQUISITE

• we can look at real world applications of hypothesis testing.

• Then begin talking about today's problem statement

Problem Statement

Problem:

• Precision is a way to measure the observational error.

Chi-Squared Probability Distribution

The chi-squared distribution is a probability distribution that is used to model the distribution of a sum of squared standard normal random variables. It is a continuous probability distribution that takes on only non-negative values.

The chi-squared distribution has a single parameter called the degrees of freedom, which determines the shape of the distribution. The degrees of freedom parameter is denoted by the symbol "k" and must be a positive integer. As k increases, the chi-squared distribution becomes more normal in shape.

Mean and Variance

Mode

Application of Chi Square Distribution

The chi-squared distribution is commonly used in hypothesis testing and in confidence interval estimation for the variance of a normally distributed population. It is also used in statistical inference for categorical data, such as testing for independence in contingency tables.

It is used for statistical tests where the test statistic follows a Chi-squared distribution. Two common tests that rely on the Chi-square distribution are the Chi-square goodness of fit test and the Chi-square test of independence.