Hypothesis Testing

Concept

​ Hypothesis testing is a fundamental concept in statistics used to determine if a claim or assumption about a parameter in a population is true, based on sample data.

In simple terms, hypothesis testing involves:

1. Setting up two opposing statements:

   • Null Hypothesis $( H_0 )$: Represents a statement of no effect or no difference.
   • Alternative Hypothesis $( H_1 )$ or $( H_a )$: Represents what we want to prove (a statement of an effect or difference).

2. Collecting and analyzing sample data.

3. Making a decision:

   • If the sample data provide sufficient evidence against $( H_0 )$, we reject the null hypothesis in favor of the alternative.
   • If not, we fail to reject the null hypothesis.

4. Drawing a conclusion:

   • Either there is enough evidence to support the claim, or there isn't.

For example, you might want to test whether a new drug is more effective than an existing one. The null hypothesis might state that the new drug has no difference in effectiveness, while the alternative hypothesis states that it does. After conducting an experiment and collecting data, you'd use hypothesis testing to decide whether to reject the null hypothesis in favor of the alternative.