Type I Error, Type II Error, and Power
A free Statistics and Data Analysis lesson from the “Inference and Conclusions” unit, with a worked example and practice problems including step-by-step solutions.
Hypothesis tests can make two kinds of errors. Type I error rejects a true null hypothesis. Type II error fails to reject a false null hypothesis. Power is the chance of detecting a real effect. This lesson builds the habit of reading the context first, choosing the right statistical tool, calculating carefully, and then writing what the result means. By the end, students should be able to do the computation and explain why that computation answers the question.
What you'll learn
- Identify Type I and Type II errors
- Connect significance level to Type I error risk
- Explain power as the chance of detecting a real effect
Worked example
Problem. A test rejects a medicine's 'no effect' null hypothesis even though the medicine truly has no effect. What kind of error is this?
- Type I error rejects a true null hypothesis.
- This is a false alarm.
Answer: Type I error
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Practice case A: A false alarm in a hypothesis test is:
Choices: Type I error · Type II error · power · confidence level
Show solution
- Type I error is a false alarm.
- It rejects a null that is actually true.
Answer: Type I error
2. Practice case B: Saying there is not enough evidence when a real effect exists is:
Choices: Type I error · alpha · placebo effect · Type II error
Show solution
- Type II error misses a real effect.
- It fails to reject a null that is false.
Answer: Type II error
3. Practice case C: Power is the probability of:
Choices: choosing a sample conveniently · proving the null true · detecting a real effect · making a Type I error
Show solution
- Power is the chance of rejecting a false null.
- That means detecting a real effect.
Answer: detecting a real effect
4. Practice case D: Using a smaller significance level mainly lowers the chance of:
Choices: the population parameter · Type I error risk · sample size · all uncertainty
Show solution
- Alpha controls the false-alarm rate.
- Lower alpha makes rejecting harder.
Answer: Type I error risk
5. Practice case E: More data often improves a test by increasing:
Choices: power · undercoverage · response bias · the null hypothesis
Show solution
- Larger samples can make real effects easier to detect.
- That raises power.
Answer: power
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