Hypothesis Testing Practice

What’s Included

This worksheet contains 20 practice problems organized into five sections:

• Section A: Setting Up Hypotheses (4 problems) — write null and alternative hypotheses for real-world scenarios, identify one-sided vs two-sided tests
• Section B: One-Sample Z-Tests (4 problems) — perform z-tests for proportions and means (sigma known), find p-values, and state conclusions
• Section C: One-Sample T-Tests (4 problems) — perform t-tests for means (sigma unknown), use the t-table, and interpret results in context
• Section D: Two-Sample Tests (4 problems) — two-sample t-tests, two-proportion z-tests, and paired t-tests for comparing groups
• Section E: Interpreting Results (4 problems) — identify Type I and Type II errors, evaluate statistical vs practical significance, and read software output

An answer key with full solutions is included on the final page.

How to Use

1. Download and print the PDF using the button above
2. Work through each section — show all steps including hypotheses, conditions, test statistic, p-value, and conclusion
3. Use the z-table and t-table provided on the worksheet (or the calculators linked below)
4. Check your answers against the answer key after completing all problems

Topics Covered

• Null and alternative hypotheses ($H_0$ and $H_a$)
• Z-test for proportions: $z = \frac{\hat{p} - p_0}{\sqrt{p_0(1-p_0)/n}}$
• T-test for means: $t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}$
• Two-sample t-test and paired t-test
• P-values and significance levels
• Type I and Type II errors
• Statistical significance vs practical significance

Related

• Introduction to Hypothesis Testing — the logic, p-values, and errors
• One-Sample Z-Tests — z-tests for proportions and means
• One-Sample T-Test — the workhorse t-test
• Two-Sample Tests — comparing two groups
• Confidence Interval Calculator — check your interval calculations