Hypothesis Testing; why and when to use.

A hypothesis is an assumption or an opinion which may or may not be true.
Hypothesis testing is a procedure which enables to decide on the basis of the information obtained from sample data whether to accept or reject an assumption about the value of a population parameter. It is a rule for deciding whether to reject o fail to reject the statistical hypothesis.
The rejection of a hypothesis is to declare it is false, while the acceptance of a hypothesis is to conclude that there is insufficient evidence to reject it but that doesn't necessary mean that the hypothesis is true.
We reject null hypothesis when it is true and this is type 1 error, and fail to reject alternative hypothesis when it is false and is called type 2 error.

Why We Use Hypothesis Testing

1. To Make Data-Driven Decisions
   It helps decision-makers rely on evidence rather than intuition or anecdotal information.

2. To Test Theories or Claims
   Researchers and analysts use hypothesis testing to determine whether there is enough evidence to support or reject a specific hypothesis about a population parameter (e.g., mean, proportion, variance).

3. To Compare Groups or Conditions
   It is commonly used to compare two or more groups (e.g., treatment vs. control) or to assess the effect of an intervention or change.

4. Business and Marketing – Helps in analyzing customer behavior, A/B testing, and making strategic decisions.

When We Use Hypothesis Testing

1. Scientific Research. To determine if a new teaching method improves student performance. 2.Business and Economics: To assess whether a marketing campaign led to a significant increase in sales.
2. Quality Control: To test whether a batch of products meets specified quality standards.
3. Machine Learning and Data Science: To test the significance of features in a predictive model.

Steps in Hypothesis Testing

1. State the Hypotheses by defining the null and alternative hypotheses.
2. Choose a Significance Level (α).
3. Select the Appropriate Test. Choose a statistical test (e.g., t-test, chi-square test, ANOVA) based on the data type and research question.
4. Calculate the Test Statistic.
5. Determine the p-value.
6. Make a Decision. Reject the null hypothesis if the p-value < α; otherwise, fail to reject it.
7. Draw Conclusions. Interpret the results in the context of the research question.

Conclusion
Hypothesis testing is a powerful tool for making informed decisions and drawing conclusions from data. It is used to test theories, compare groups and validate assumptions. It has its limitations thus interpreting results carefully, considering the context and underlying assumptions. Hypothesis testing helps bridge the gap between data and actionable insights.