## Hypothesis Testing :

Hypothesis testing is a statistical method used to determine whether or not a certain hypothesis about a population is true. It is an essential tool in statistical analysis, and is used to make decisions about a population based on sample data.

To understand hypothesis testing, let’s first define some key terms. The null hypothesis is a statement that assumes that there is no difference between the population and the sample. The alternative hypothesis is the opposite of the null hypothesis, and asserts that there is a difference between the population and the sample. In other words, the null hypothesis is the “default” assumption, while the alternative hypothesis is what we are trying to prove.

To conduct a hypothesis test, we first need to collect a sample from the population. Then, we compute a test statistic based on the sample data. This test statistic is a numerical value that can be compared to a reference value, known as the critical value, to determine whether or not the null hypothesis can be rejected.

Here are two examples of hypothesis testing:

A medical researcher wants to determine if a new drug is effective at lowering blood pressure. The null hypothesis is that the new drug has no effect on blood pressure, while the alternative hypothesis is that the new drug does lower blood pressure. The researcher randomly assigns patients to receive either the new drug or a placebo, and then measures their blood pressure after a certain period of time. Based on the sample data, the researcher computes a test statistic and compares it to the critical value. If the test statistic is greater than the critical value, the null hypothesis is rejected and the alternative hypothesis is accepted.

Another example of hypothesis testing is in the field of psychology. A researcher wants to determine if there is a difference in anxiety levels between men and women. The null hypothesis is that there is no difference in anxiety levels between the two groups, while the alternative hypothesis is that there is a difference. The researcher collects a sample of men and women, and administers a standardized anxiety test to each participant. The researcher then calculates a test statistic, such as the difference in mean anxiety levels between the two groups, and compares it to the critical value. If the test statistic is significantly different from the critical value, the null hypothesis is rejected and the alternative hypothesis is accepted.

In conclusion, hypothesis testing is a statistical method used to determine whether or not a certain hypothesis about a population is true. It involves collecting a sample from the population, calculating a test statistic based on the sample data, and comparing the test statistic to a critical value. If the test statistic is significantly different from the critical value, the null hypothesis is rejected and the alternative hypothesis is accepted. Hypothesis testing is an important tool in making decisions about a population based on sample data.