Figuring out exactly what the **null hypothesis** and the **alternative hypotheses** are, is not a walk in the park. **Hypothesis** testing is based on the knowledge that you can acquire by going over what we have previously covered about statistics in our blog.

So, if you don’t want to have a hard time keeping up, make sure you have read all the tutorials about **confidence intervals**, **distributions**, **z-tables** and **t-tables**.

**Confidence intervals** provide us with an estimation of where the parameters are located.

However, when we are making a decision, we need a yes or no answer. The correct approach, in this case, is to use a *test*.

Here we will start learning about one of the fundamental tasks in statistics – **hypothesis testing**!

**Data-Driven Decision-Making**

First off, let’s talk about data-driven decision-making. It consists of the following steps:

- First, we must formulate a
**hypothesis**. - After doing that, we have to find the right test for our
**hypothesis**. - Then, we execute the test.
- Finally, we make a decision based on the result.

Let’s start from the beginning.

**What is a Hypothesis?**

Though there are many ways to define it, the most intuitive must be:

“A hypothesis is an idea that can be tested.”

This is not the formal definition, but it explains the point very well.

So, if we say that apples in New York are expensive, this is an idea or a statement. However, it is not testable, until we have something to compare it with.

For instance, if we define expensive as: any price higher than $1.75 dollars per pound, then it immediately becomes a **hypothesis**.

**What Cannot Be a Hypothesis?**

An example may be: would the USA do better or worse under a Clinton administration, compared to a Trump administration? Statistically speaking, this is an *idea*, but there is no data to test it. Therefore, it cannot be a **hypothesis** of a statistical test.

Actually, it is more likely to be a topic of another discipline.

Conversely, in statistics, we may compare different US presidencies that have already been completed. For example, the Obama administration and the Bush administration, as we have data on both.

**A Two-Sided Test**

Alright, let’s get out of politics and get into **hypotheses**. Here’s a simple topic that **CAN** be tested.

According to Glassdoor (the popular salary information website), the **mean** data scientist salary in the US is 113,000 dollars.

So, we want to test if their **estimate** is correct.

**The Null and Alternative Hypotheses**

There are two **hypotheses** that are made: the **null hypothesis**, denoted H_{0}, and the **alternative hypothesis**, denoted H_{1}or H_{A}.

The **null hypothesis** is the one to be tested and the **alternative** is everything else. In our example,

The **null hypothesis** would be: The **mean** data scientist salary is 113,000 dollars.

While the **alternative**: The **mean** data scientist salary is not 113,000 dollars.

**The Concept of the Null Hypothesis**

Now, you would want to check if 113,000 is close enough to the true **mean**, predicted by our sample. In case it is, you would ** accept** the

**null hypothesis**. Otherwise, you would

**the**

*reject***null hypothesis**.

The concept of the **null hypothesis** is similar to: innocent until proven guilty. We assume that the **mean** salary is 113,000 dollars and we try to prove otherwise.

This is called a *two-sided* or а *two-tailed* test.

**An Example of a One-Sided Test**

You can also form *one-sided* or *one-tailed* tests.

Say your friend, Paul, told you that he thinks data scientists earn more than 125,000 dollars per year. You doubt him, so you design a test to see who’s right.

The **null hypothesis** of this test would be: The **mean** data scientist salary is more than 125,000 dollars.

The **alternative** will cover everything else, thus: The **mean** data scientist salary is less than or equal to 125,000 dollars.

**Important:** The outcomes of tests refer to the population parameter rather than the sample statistic! So, the result that we get is for the population.

**Important:** Another crucial consideration is that, generally, the researcher is trying to reject the **null hypothesis**. Think about the **null hypothesis** as the status quo and the **alternative** as the change or innovation that challenges that status quo. In our example, Paul was representing the status quo, which we were challenging.

Let’s go over it once more. In statistics, the **null hypothesis** is the statement we are trying to reject. Therefore, the **null hypothesis** is the present state of affairs, while the **alternative** is our personal opinion.

**Why Hypothesis Testing Works**

Right now, you may be feeling a little puzzled. This is normal because this whole concept is counter-intuitive at the beginning. However, there is an extremely easy way to continue your journey of exploring it. By diving into the linked tutorial, you will find out why **hypothesis** testing actually works.

**Next Tutorial: **Hypothesis Testing: Significance Level and Rejection Region