Classification of Statistical Hypotheses
The best way to decide if a statistical hypothesis is correct is to look at the population as a whole. In most cases, this is not feasible, so researchers usually study a random sample from a population. If the obtained results do not match the statistical hypothesis, the hypothesis is rejected.

There are two types of statistical hypotheses.

null hypothesis: denoted by H0, usually hypotheses derived from pure probability.
An alternative hypothesis, denoted H1 or Ha, is that some non-random factor influences the sample observations.
For example, suppose we want to decide if a coin is uniform and balanced. One possible null hypothesis is that Half of the tosses will be tails, the Other Half will be heads. The converse hypothesis is that the number of heads and tails will be very different.

We denote it as follows:

H0: P = 0.5

Ha: P 0.5

Let’s say we toss a coin 50 times, 40 heads, ten tails. If this result is obtained, we are inclined to reject the null hypothesis. We can conclude, based on the evidence obtained, that the coin may be heterogeneous and disproportionate.

Can we accept the hypothesis?
Some researchers say that a hypothesis test can have two outcomes: accept the null hypothesis or reject the null hypothesis. Many statisticians are more cautious about using the phrase “accept the null hypothesis.” Instead, they say: reject the null hypothesis or fail to reject the null hypothesis.

Why is there a distinction between “acceptance” and “failure to reject”? Acceptance implies that the hypothesis is not valid. Failure to reject implies that the data we have is not convincing enough to choose the negative hypothesis over the null hypothesis.

The process of testing a statistical hypothesis.
Statisticians follow a standard process for deciding to reject a null hypothesis based on a sample of data. This process, called hypothesis testing, consists of the following four steps:

Make hypotheses. This step aims to show what is a null hypothesis and which is an inverse hypothesis. Hypotheses are posed in a mutually exclusive manner. That is, if one is true, then the other must be false.
Develop an analysis plan. The analysis plan describes how the sample data will be used to evaluate the null hypothesis. Evaluation is usually centered around a single test statistic.
Analyze sample data. Find the values ​​of the sample statistic (mean, ratio, t-statistic, z-score, etc.) described in the analysis plan.
Read the results. Apply the decision rules described in the analysis plan. If the obtained results do not match the null hypothesis, the null hypothesis is rejected.
Types of errors when making decisions
Type I error (Type I error). Type 1 errors occur when researchers reject a null hypothesis when it is true. The probability of encountering a type 1 error is called the significance level. This probability is also called alpha, usually denoted α .
Type 2 error (Type II error). Type 2 errors occur when researchers fail to disprove a null hypothesis while it is false. The probability of making a type 2 error is called Beta, denoted by β. The probability of not making a type 2 error is called the Power of the test.