Null and Alternative Hypothesis Worksheet- Practice Problems

Null and Alternative Hypothesis Worksheet: Practice Problems That Actually Work

You need to master null and alternative hypotheses. There's no way around it. If you're taking statistics, this is the foundation everything else builds on. Mess this up, and you'll fail the entire course.

This worksheet gives you real practice problems with solutions. No fluff. No lengthy explanations of why statistics matters. Just problems, answers, and the reasoning behind them.

Quick Refresher: What You're Actually Dealing With

Before diving in, let's make sure you understand the terminology. Most students confuse these terms or memorize them without comprehension.

Null Hypothesis (H₀)

The null hypothesis states that no difference or no relationship exists in your population. It's the default assumption—the status quo. When you test a hypothesis, you're trying to prove this wrong.

Examples:

• The mean height of men equals the mean height of women
• A new drug has no effect on blood pressure
• The coin is fair (50/50 probability)

Alternative Hypothesis (H₁ or Ha)

The alternative hypothesis is what you're actually trying to prove. It states that a difference or relationship exists. This is what you accept if the data gives you enough evidence against the null.

Examples:

• The mean height of men differs from the mean height of women
• A new drug lowers blood pressure
• The coin is biased (not 50/50)

One-Tailed vs. Two-Tailed Tests

This trips up more students than almost anything else.

• Two-tailed test: You're testing for any difference (greater OR less than). H₁: μ₁ ≠ μ₂
• One-tailed test: You're testing for a difference in a specific direction. H₁: μ₁ > μ₂ or H₁: μ₁ < μ₂

Your alternative hypothesis determines which type of test you run. Choose wrong, and your entire analysis is incorrect.

Practice Problems: Test Yourself First

Try solving these before checking the answers. That's the only way this worksheet helps you.

Problem 1: The Coffee Study

A researcher claims that drinking coffee increases reaction time. She tests this by measuring reaction times of 50 people before and after drinking two cups of coffee.

Write the null and alternative hypotheses.

Problem 2: The Teaching Method

A school district wants to know if a new teaching method improves test scores. The old method had an average score of 75. The new method is tested on 200 students.

Write the null and alternative hypotheses.

Problem 3: The Manufacturing Defects

A factory claims its defect rate is less than 5%. A quality inspector suspects the rate is actually higher. She inspects 500 products and finds 35 defects.

Write the null and alternative hypotheses.

Problem 4: The Gender Pay Gap

A sociologist wants to test whether men and women earn different salaries at a company. She collects salary data from 100 men and 100 women.

Write the null and alternative hypotheses.

Problem 5: The Diet Pill

A company claims their diet pill helps people lose more than 10 pounds on average. A medical journal wants to verify this claim.

Write the null and alternative hypotheses.

How To Write Hypotheses: Step-by-Step

Most textbooks overcomplicate this. Here's the actual process:

1. Identify the population parameter (μ for means, p for proportions, μ₁ - μ₂ for comparing groups)
2. Translate the research question into a claim about that parameter
3. Write H₀ as the baseline—no effect, no difference, equality
4. Write H₁ as what you're trying to prove (difference, increase, decrease)
5. Determine the tail—is the claim directional? If yes, one-tailed. If no, two-tailed.

Common Mistakes Students Make

These errors will cost you points. Stop making them.

• Writing H₁ as "no difference"—that's H₀. H₁ is what you're trying to prove.
• Using the wrong tail—if the claim says "different," you need two tails. "Greater" or "less" means one tail.
• Confusing sample statistics with population parameters—use μ and p in hypotheses, not x̄ and p̂.
• Forgetting to define your parameters—if you're comparing two means, define what μ₁ and μ₂ represent.
• Making H₀ too specific—H₀ should contain the equality condition. "μ = 0" is sometimes right, but "μ ≥ 0" or "μ ≤ 0" is often more appropriate.

Hypothesis Types Reference Table

More Practice: Fill in the Blanks

For each scenario, write H₀ and H₁, then identify if it's one or two-tailed.

Scenario A

A psychologist tests whether background music affects test performance. She believes music will lower scores.

Your answer:

H₀: _______________

H₁: _______________

Tail: _______________

Scenario B

A company claims their batteries last exactly 100 hours. A consumer group suspects otherwise.

Your answer:

H₀: _______________

H₁: _______________

Tail: _______________

Scenario C

A fitness app claims users lose at least 5 pounds in 30 days. Users complain the results are worse.

Your answer:

H₀: _______________

H₁: _______________

Tail: _______________

How To Check Your Work

Before submitting any hypothesis test, verify these conditions:

• H₀ contains the equality sign (=, ≥, or ≤)
• H₁ does not contain equality (≠, >, or <)
• The direction matches the claim—if you're testing "increases," H₁ should use ">"
• Parameters are defined—readers know what μ or p represents
• The test matches the research question—not what you wish the question was asking

The Bottom Line

Writing null and alternative hypotheses is straightforward once you understand the logic. H₀ is the boring status quo. H₁ is the interesting claim you're investigating. Match the symbols to the direction of the effect, and you'll get it right every time.

Practice these problems until you can write them in your sleep. Hypothesis testing problems on exams are usually just variations of the same patterns. Learn the patterns.