**hypothesis**testing works, you should first have an idea about the

**significance level**and the

**reject region**. We assume you already know what a

**hypothesis**is, so let’s jump right into the action.

**What Is the Significance Level?**

First, we must define the term **significance level**. Normally, we aim to reject the null if it is false.

**null hypothesis**that is true.

**How Is the Significance Level Denoted?**

The **significance level**is denoted by

*α*and is the probability of rejecting the

**null hypothesis**, if it is true.

*α*are 0.01, 0.05 and 0.1. It is a value that we select based on the certainty we need. In most cases, the choice of

*α*is determined by the context we are operating in, but 0.05 is the most commonly used value.

**A Case in Point**

Say, we need to test if a machine is working properly. We would expect the test to make little or no mistakes. As we want to be very precise, we should pick a low **significance level**such as 0.01. The famous Coca Cola glass bottle is 12 ounces. If the machine pours 12.1 ounces, some of the liquid would be spilled, and the label would be damaged as well. So, in certain situations, we need to be as accurate as possible.

**Higher Degree of Error**

However, if we are analyzing humans or companies, we would expect more random or at least uncertain behavior. Hence, a higher degree of error.
**significance level**like 0.05 or 0.1.

## Hypothesis Testing: Performing a Z-Test

Now that we have an idea about the**significance level**, let’s get to the mechanics of hypothesis testing. Imagine you are consulting a university and want to carry out an analysis on how students are performing on average.

**null hypothesis**is: The population mean grade is 70%. This is a hypothesized value. The

**alternative hypothesis**is: The

**population mean**grade is not 70%. You can see how both of them are denoted, below.

**Visualizing the Grades**

Assuming that the population of grades is normally distributed, all grades received by students should look in the following way.
**population mean**.

**Performing a Z-test**

Now, a test we would normally perform is the *Z-test*. The formula is:

*Z*equals the

**sample mean**, minus the

**hypothesized mean**, divided by the

**standard error**.

**sample mean**we got. If the

**sample mean**is close enough to the

**hypothesized mean**, then

*Z*will be close to 0. Otherwise, it will be far away from it. Naturally, if the

**sample mean**is exactly equal to the

**hypothesized mean**,

*Z*will be 0.

**the**

*accept***null hypothesis**.

### What Is the Rejection Region?

The question here is the following: How big should*Z*be for us to

**reject**the

**null hypothesis**? Well, there is a cut-off line. Since we are conducting a

*two-sided*or a

*two-tailed*test, there are two cut-off lines, one on each side.

*Z*, we will get a value. If this value falls into the middle part, then we

*cannot*reject the null. If it falls outside, in the shaded region, then we reject the

**null hypothesis**. That is why the shaded part is called:

**rejection region**, as you can see below.

**What Does the Rejection Region Depend on?**

The area that is cut-off actually depends on the **significance level**. Say the

**level of significance**,

*α*, is 0.05. Then we have

*α*divided by 2, or 0.025 on the left side and 0.025 on the right side.

*z-table*. When

*α*is 0.025,

*Z*is 1.96. So, 1.96 on the right side and minus 1.96 on the left side. Therefore, if the value we get for

*Z*from the test is lower than minus 1.96, or higher than 1.96, we will reject the

**null hypothesis**. Otherwise, we will accept it.

**sample mean**with respect to the hypothesized value. If Z is close to 0, then we cannot reject the null. If it is far away from 0, then we reject the

**null hypothesis**.

## Example of One Tailed Test

What about one-sided tests? We have those too! Let’s consider the following situation. Paul says data scientists earn more than $125,000. So, H_{0}is: μ

_{0}is bigger than $125,000. The

**alternative**is that μ

_{0}is lower or equal to 125,000. Using the same

**significance level**, this time, the whole

**rejection region**is on the left. So, the

**rejection region**has an area of

*α*. Looking at the z-table, that corresponds to a

*Z*-score of 1.645. Since it is on the left, it is with a minus sign.

**Accept or Reject**

Now, when calculating our test statistic *Z*, if we get a value lower than -1.645, we would reject the

**null hypothesis**. We do that because we have statistical evidence that the data scientist salary is less than $125,000. Otherwise, we would accept it.

**Another One-Tailed Test**

To exhaust all possibilities, let’s explore another *one-tailed*test. Say the university dean told you that the average GPA students get is lower than 70%. In that case, the

**null hypothesis**is: μ

_{0}is lower than 70%. While the

**alternative**is: μ

_{0`}is bigger or equal to 70%.

**rejection region**is on the right side. So, if the test statistic is bigger than the cut-off z-score, we would reject the null, otherwise, we wouldn’t.

## Importance of the Significance Level and the Rejection Region

To sum up, the**significance level**and the

**reject region**are quite crucial in the process of hypothesis testing. The level of significance conducts the accuracy of prediction. We (the researchers) choose it depending on how big of a difference a possible error could make. On the other hand, the

**reject region**helps us decide whether or not to reject the

**null hypothesis**. After reading this and putting both of them into use, you will realize how convenient they make your work. The article first appeared on: https://365datascience.com/significance-level-reject-region/

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