Worksheets · Statistics

Hypothesis testing worksheet

The null hypothesis is the claim being tested and always has the equals sign. A p-value below α is evidence against it: reject H₀. Rejecting a true H₀ is a Type I error; failing to reject a false one is a Type II error.

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Name

Hypothesis Tests

Date Period

Answer each question.

  1. H0: p=0.5. In a random sample of 100, p^=0.55. Find the test statistic z
  2. A test gives a p-value of 0.04. At α=0.1, what is the decision?
  3. H0: p=0.5. In a random sample of 400, p^=0.475. Find the test statistic z
  4. A test gives a p-value of 0.07. At α=0.01, what is the decision?
  5. A coin is supposed to land heads half the time. A student suspects it is unfair. State the hypotheses.
  6. A company claims 60% of customers are satisfied. A consumer group suspects the true share is lower. State the hypotheses.
  7. H0: p=0.5. In a random sample of 100, p^=0.45. Find the test statistic z
  8. A test gives a p-value of 0.02. At α=0.05, what is the decision?
  9. H0: p=0.5. In a random sample of 400, p^=0.4625. Find the test statistic z
  10. A factory says 5% of its bulbs are defective. An inspector suspects the rate is higher. State the hypotheses.
  11. H0: p=0.5. In a random sample of 400, p^=0.45. Find the test statistic z
  12. A test gives a p-value of 0.008. At α=0.01, what is the decision?
  13. Last year 30% of students walked to school. The principal thinks the share has risen. State the hypotheses.
  14. H0: p=0.4. In a random sample of 96, p^=0.3. Find the test statistic z
  15. A test gives a p-value of 0.02. At α=0.01, what is the decision?
  16. H0: p=0.1. In a random sample of 900, p^=0.085. Find the test statistic z
  17. A test gives a p-value of 0.07. At α=0.1, what is the decision?
  18. A test gives a p-value of 0.3. At α=0.1, what is the decision?
  19. A test gives a p-value of 0.06. At α=0.1, what is the decision?
  20. A test gives a p-value of 0.06. At α=0.05, what is the decision?

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Hypothesis TestsAnswer keyVersion 1

Date Period

Answer each question.

  1. H0: p=0.5. In a random sample of 100, p^=0.55. Find the test statistic z1
  2. A test gives a p-value of 0.04. At α=0.1, what is the decision?Reject H0
  3. H0: p=0.5. In a random sample of 400, p^=0.475. Find the test statistic z−1
  4. A test gives a p-value of 0.07. At α=0.01, what is the decision?Fail to reject H0
  5. A coin is supposed to land heads half the time. A student suspects it is unfair. State the hypotheses.H0: p=0.5; Ha: p≠0.5
  6. A company claims 60% of customers are satisfied. A consumer group suspects the true share is lower. State the hypotheses.H0: p=0.6; Ha: p<0.6
  7. H0: p=0.5. In a random sample of 100, p^=0.45. Find the test statistic z−1
  8. A test gives a p-value of 0.02. At α=0.05, what is the decision?Reject H0
  9. H0: p=0.5. In a random sample of 400, p^=0.4625. Find the test statistic z−1.5
  10. A factory says 5% of its bulbs are defective. An inspector suspects the rate is higher. State the hypotheses.H0: p=0.05; Ha: p>0.05
  11. H0: p=0.5. In a random sample of 400, p^=0.45. Find the test statistic z−2
  12. A test gives a p-value of 0.008. At α=0.01, what is the decision?Reject H0
  13. Last year 30% of students walked to school. The principal thinks the share has risen. State the hypotheses.H0: p=0.3; Ha: p>0.3
  14. H0: p=0.4. In a random sample of 96, p^=0.3. Find the test statistic z−2
  15. A test gives a p-value of 0.02. At α=0.01, what is the decision?Fail to reject H0
  16. H0: p=0.1. In a random sample of 900, p^=0.085. Find the test statistic z−1.5
  17. A test gives a p-value of 0.07. At α=0.1, what is the decision?Reject H0
  18. A test gives a p-value of 0.3. At α=0.1, what is the decision?Fail to reject H0
  19. A test gives a p-value of 0.06. At α=0.1, what is the decision?Reject H0
  20. A test gives a p-value of 0.06. At α=0.05, what is the decision?Fail to reject H0

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

A p-value of 0.03 at α=0.05

  1. 0.03 is less than 0.05.

The answer is Reject H0.

Where students go wrong

Writing "accept H₀". A test that fails to reject has only failed to find evidence; it has not shown the null is true.

Also called significance test, null and alternative hypotheses, p-value or type I and type II errors.

Questions about these worksheets

Yes. Every hypothesis testing sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Statistics is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the hypothesis testing questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Writing "accept H₀". A test that fails to reject has only failed to find evidence; it has not shown the null is true.