Using Inferential Statistics, we learned how to analyze the sample data and make inferences about the population mean and other population data. However, we could not confirm the conclusions we made about the population data. That is why the concept of Hypothesis Testing comes into the picture.

You can find out more about Inferential Statistics and Central Limit Theorem in my previous articles.

### Hypothesis

Using Inferential, Descriptive, and Exploratory analysis, we performed some research on the population sample. We derived some insights from the sample and made claims about the entire population. These are just the claims; they are not exactly true. This type of claim or assumption is called Hypothesis.

### Hypothesis Testing

There are some ways or tricks to check the Hypothesis, and if the hypothesis is correct, then we apply it to the whole population. This process is known as **Hypothesis Testing. **The final goal is whether there is enough evidence that the hypothesis is correct. As we have already seen in Inferential Statistics and Central Limit Theorem(CLT), we will work with sample data and confirm our assumption about the population in Hypothesis Testing.

In Hypothesis Testing, we formulate two hypotheses:

• Null Hypothesis (H₀): Status quo
• Alternate Hypothesis (H₁): It challenges the status quo

### Null Hypothesis (H₀)

The null hypothesis is the prevailing belief about a population. It states that there is no change or no difference in the situation or the claim. H₀ denotes the null hypothesis.

### Alternate Hypothesis (H₁)

The alternate hypothesis is the claim that opposes the null hypothesis. H₁ denotes an alternate hypothesis.

For Example, in a criminal trial, the jury has to decide whether the defendant is innocent or guilty for a case. Here the null hypothesis is, the defendant is innocent just like before the charges. The alternate hypothesis is the defendant is guilty, and the prosecutor would try to prove this.

### The outcome of Hypothesis Testing

In hypothesis testing, we reject the null hypothesis if there is sufficient evidence to support the alternate hypothesis. If there is no sufficient evidence for the alternate hypothesis, we fail to reject the null hypothesis. That is how we make claims. In any case, we should never say that we “accept” the null hypothesis. Either we reject, or we fail to reject the null hypothesis, that’s it.

Example:

If a company has 30000 employees and claims that it takes an average of 35 minutes for the employees to reach the office daily.

Here,

The Null Hypothesis(H₀): Average time for employees = 35 minutes

The Alternate Hypothesis(H₁): Average time for employees ≠ 35 minutes

#hypothesis-testing #critical-value #inferential-statistics #p-value #data-science

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