Hypothesis testing

is a fundamental concept in statistics used to make inferences about population parameters based on
sample data. Here's a general overview of hypothesis testing:

1.    Formulating Hypotheses:

o   We start with two mutually exclusive hypotheses:

§  Null Hypothesis (H0): It represents the status quo or no effect, stating that there is no
difference or no effect in the population.

§    Alternative Hypothesis (H1 or Ha): It contradicts the null hypothesis, suggesting that there
is a difference, effect, or relationship in the population.


2.    Choosing a Test Statistic:

o   Based on the nature of the data and the research question, we choose an appropriate test
statistic. Common test statistics include t-test, chi-square test, ANOVA, correlation coefficient,
etc.


3.    Setting Significance Level (α):

o   Significance level (α) is the probability of rejecting the null hypothesis when it is actually
true. It is usually set to 0.05 or 0.01, representing a 5% or 1% chance of making a Type I error,
respectively.


4.    Collecting Data and Calculating Test Statistic:

o   Data is collected from a sample, and the test statistic is calculated based on this sample.


5.    Determining Critical Value or P-value:

o   Depending on the test statistic chosen, we determine either a critical value from the
statistical distribution or calculate the p-value.


6.    Making a Decision:

o   If the test statistic falls in the rejection region (beyond the critical value) or if the
p-value is less than the significance level, we reject the null hypothesis in favor of the
alternative hypothesis. Otherwise, we fail to reject the null hypothesis.


7.    Drawing Conclusion:

o   Based on our decision, we draw conclusions about the population parameter. If the null
hypothesis is rejected, we conclude that there is evidence to support the alternative hypothesis.
If the null hypothesis is not rejected, we conclude that there is not enough evidence to support
the alternative hypothesis.

Hypothesis testing is a powerful tool used in various fields such as science, business, medicine,
and social sciences to draw meaningful conclusions from data.