At the heart of every hypothesis test are two competing statements about a population:

• The null hypothesis
• The alternative hypothesis

They must be:
Mutually exclusive (can’t both be true)
Exhaustive (cover all possibilities)
About population parameters, not sample statistics

Let’s break down how to set them up correctly.

🎯 1. Start with the research question

Ask yourself: What am I trying to show, detect, or test?

• If you want to show a difference → contains the difference
• If you want to show an increase → contains “>”
• If you want to show a decrease → contains “<”

The alternative hypothesis always reflects the researcher’s suspicion or claim.

🎯 2. The null hypothesis is the “no effect” or “no difference” statement

It usually states:

• equality
• no change
• no relationship
• no improvement

Examples:

• 
• 
• 

The null is the default assumption — the thing you try to find evidence against.

🎯 3. Choose the correct form of the alternative hypothesis

There are three types:

A. Two‑tailed test (difference in either direction)

Use when you care about any difference.

Example:
“Is the average score different from 70?”

B. Right‑tailed test (greater than)

Use when you want to show an increase.

Example:
“Does the new fertilizer increase plant height?”

C. Left‑tailed test (less than)

Use when you want to show a decrease.

Example:
“Is the average waiting time shorter than 10 minutes?”

🎯 4. Make sure hypotheses are about population parameters

Correct:

• 
• 

Incorrect:

• 
• 

Sample statistics belong in the test statistic, not the hypotheses.

🎯 5. Keep the null hypothesis with equality

The null always includes the equality sign:

• 
• 
• 

The alternative never includes equality.

⭐ Fresh, Original Examples

Example 1: Testing a Mean

Claim: The average battery life is 10 hours.

Example 2: Testing for an Increase

A teacher believes a new method improves test scores.

Example 3: Testing a Proportion

A company claims 40% of customers choose the premium plan.

Example 4: Comparing Two Groups

Do men and women have different average daily step counts?

Example 5: Paired Test (Before/After)

Does a training program reduce reaction time?

(where is the mean of the differences)

🎨 The Big Idea

Setting up hypotheses is about:

• translating a research question into math
• deciding what “no effect” looks like
• deciding what kind of effect you’re testing for

Once the hypotheses are set, the rest of the test flows naturally.