Hello everyone, today I want post about Hypotheses Testing,

A key idea in data analysis and statistical inference is hypothesis testing. Based on sample data, statistical conclusions about population parameters are drawn. Generally, the procedure goes like this:

Construct Hypotheses:

The null hypothesis (H0) asserts that there is no difference or effect. It stands for the current situation or the presumption that nothing will change or have an impact.
Hypothesis Alternative (H1 or Ha): This assertion runs counter to the null hypothesis. It stands for the assertion or claim that there is a notable impact or distinction.
Select the Level of Significance (α):

The probability of rejecting the null hypothesis in the event that it is true is known as the significance level (α). Typically, α is set to 0.05, 0.01, or 0.10.

Collect and Analyze Data:

Gather information that is pertinent to the hypothesis being investigated.

Determine the Test Statistic and P-value:

Find the P-value and test statistic:

A numerical value derived from the sample data is the test statistic. With the assumption that the null hypothesis is correct, its distribution is known.
Assuming the null hypothesis is true, the p-value is the likelihood of finding a test statistic that is as extreme as or more extreme than the one derived from the sample data.

Make a Decision:

The alternative hypothesis is accepted and the null hypothesis is rejected if the p-value is less than or equal to the selected significance level (α).
If the null hypothesis cannot be rejected due to insufficient evidence, the p-value must be greater than the significance level.
Draw Inferences:

Draw conclusions about the population parameter under test based on the choice made in step 5.

Errors of Type I and Type II:

Rejecting the null hypothesis when it is true is a Type I Error (False Positive).
False Negative Type II Error: Rejecting the null hypothesis when it is false.
Confidence Intervals

Building confidence intervals is a useful addition to testing hypotheses. Further support for the null hypothesis is given if it is associated with a parameter that falls within the confidence interval.

Common statistical tests used in hypothesis testing include:

T-tests: A method for comparing two groups’ means.
The Analysis of Variance, or ANOVA, is used to compare the means of multiple groups.
Chi-square tests: utilized in the analysis of categorical data.
Z-tests: When the population standard deviation is known or when sample sizes are large.
A popular technique for making decisions based on data, hypothesis testing is utilized in many disciplines, including data science, psychology, economics, and medicine.