Inferential Statistics • Lesson 11

Hypothesis Testing

Learn how statisticians use sample data to evaluate claims about a population and make evidence-based statistical decisions.

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Concept 1POPULATION CLAIM

Start With a Population Claim

Hypothesis testing begins with a claim about a population. We collect sample data and use that evidence to evaluate whether the sample result is compatible with the population claim.

Learn by seeing

Claim → Sample Data → Decision

Population
Business Claim
        ↓
     Sample
Sample Data
        ↓
 Test Statistic
        ↓
 Evidence
        ↓
 Statistical Decision

The process begins with a claim about a population and uses sample evidence to evaluate that claim.

🌍

Population

μ = 30 minutes

🔎

Sample

Delivery-time data

🎯

Decision

Evaluate the claim

Analyst workflow

Complete hypothesis testing workflow

1. Define the population question.

2. State H₀ and Hₐ before examining the result.

3. Choose the appropriate test.

4. Set the significance level α.

5. Collect and analyze the sample.

6. Calculate the test statistic.

7. Evaluate the evidence.

8. Reject or fail to reject H₀.

9. State the conclusion in the original context.

Lesson summary

Remember these ideas

✓ Hypothesis testing evaluates a population claim using sample evidence.

✓ H₀ represents the baseline or null hypothesis.

✓ Hₐ represents the competing hypothesis.

✓ The test statistic measures the observed difference relative to sampling variability.

✓ A predefined rule is used to make the statistical decision.

✓ Reject H₀ means sufficient evidence against H₀ under the chosen procedure.

✓ Fail to reject H₀ does not prove H₀ true.

✓ The final conclusion should be stated in the original context.