Advanced Hypothesis Testing
ChiSquare 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.
ChiSquared Probability Distribution
The chisquared 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 nonnegative values.
The chisquared 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 chisquared distribution becomes more normal in shape.
Mean and Variance
Mode
Application of Chi Square Distribution
The chisquared 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 Chisquared distribution. Two common tests that rely on the Chisquare distribution are the Chisquare goodness of fit test and the Chisquare test of independence.