Type I Error in AP Statistics

In AP Statistics, a Type I error happens when you reject a null hypothesis that is actually true. It's a false positive: you conclude there's evidence for the alternative when there isn't. If H₀ is true, the probability of a Type I error equals the significance level, α.

What is Type I Error?

A Type I error is the mistake of rejecting H₀ when H₀ is actually true. Think of it as a false alarm. Your sample data looked unusual enough to cross your cutoff, so you declared there's convincing evidence of an effect. In reality, the null was right all along, and you just got an unlucky sample.

The key number is the significance level (α). You reject H₀ whenever your p-value is at or below α. So if H₀ really is true, the chance you reject it anyway is exactly α. Set α = 0.05 and you've accepted a 5% risk of a false positive. One more detail matters: a Type I error can only happen when you reject H₀. If you fail to reject, the only error you could be making is a Type II error.

Why Type I Error matters in AP® Statistics

Type I error lives in Topic 3.8, Potential Errors When Performing Tests. Use the study guide for that topic for the full picture. This term matters because it turns α from a random rule ("use 0.05") into a real decision about risk. Choosing α means choosing how often you're willing to raise a false alarm. That choice pushes on everything else in the error framework. A smaller α means fewer Type I errors, but it also means more Type II errors and less power. On the exam, you'll need to describe a Type I error in the context of a specific problem, pick out its probability, and explain what happens to the other errors when α changes.

How Type I Error connects across the course

Type II Error and the α trade-off (Topic 3.8)

Type I and Type II errors sit on a seesaw. Lower α and you make it harder to reject H₀. That cuts false positives, but it also means you'll miss more real effects. With the sample size fixed, you can't shrink both errors at once just by moving α.

Power (Topic 3.8)

Power is the probability of correctly rejecting a false H₀, which is 1 − P(Type II error). Raising α from 0.01 to 0.05 increases power. The price is a higher Type I error rate, so a more powerful test is also a more "trigger-happy" one.

Null Hypothesis and significance testing (Topic 3.8)

Every Type I error is a statement about H₀. It assumes H₀ is true and asks what goes wrong if you reject it. Write H₀ clearly in terms of the parameter, and describing the error in context becomes a fill-in-the-blank.

Standard Error and sample size (Topic 3.8)

Bigger samples shrink the standard error. For example, σ = 20 and n = 64 gives 20/√64 = 2.5. That makes the test better at detecting real differences, which lowers P(Type II error). P(Type I error) stays at α, though, because you set α yourself.

Is Type I Error on the AP® Statistics exam?

Type I error shows up in both multiple choice and free response.

Multiple choice. Stems ask you to:

• match a description to the correct error ("Which statement correctly relates the null hypothesis to potential errors?")
• state that P(Type I error) = α, such as α = 0.01 in a medication study
• predict what happens when α changes (for example, raising α from 0.01 to 0.05 raises P(Type I error) and lowers P(Type II error))

Some questions give P(Type I error) = 0.05 in a two-tailed test of H₀: μ = 200 and then ask you to work toward P(Type II error) for a specific true mean, like 205.

Free response. The 2025 FRQ Q5 used this term. Its setup was a test of whether the mean number of bedrooms in newly built houses had changed from a 2017 national survey value of 2.9. The typical task in a question like this is to describe a Type I error in context. Name the parameter, say what's actually true (H₀), and say what you wrongly conclude (Hₐ). A strong answer sounds like this: "The researcher concludes the mean number of bedrooms differs from 2.9 when it really is 2.9." Generic answers like "rejecting a true null" with no context usually lose credit.

Type I Error vs Type II Error

A Type I error is a false positive. H₀ is true, and you reject it. A Type II error is a false negative. H₀ is false, and you fail to reject it. Here's a quick check. If your decision was "reject," the only possible mistake is Type I. If your decision was "fail to reject," the only possible mistake is Type II. P(Type I) is α, which you choose. P(Type II) depends on the true parameter value, the sample size, and α.

Key things to remember about Type I Error

• A Type I error means rejecting the null hypothesis when the null hypothesis is actually true, which is a false positive.

• If the null hypothesis is true, the probability of making a Type I error equals the significance level α.

• A Type I error can only happen when you reject H₀, never when you fail to reject it.

• Lowering α reduces the chance of a Type I error but increases the chance of a Type II error and lowers power, as long as the sample size stays the same.

• Increasing the sample size lowers the probability of a Type II error, but it does not change the probability of a Type I error, which stays at α.

• On free-response questions, describe a Type I error in context by naming the parameter, stating what is actually true, and stating the wrong conclusion you reach.

Frequently asked questions about Type I Error

What is a Type I error in AP Statistics?

A Type I error is rejecting a null hypothesis that is actually true. You conclude there's convincing evidence for the alternative when there isn't. Its probability, assuming H₀ is true, equals the significance level α.

Is the probability of a Type I error the same as alpha?

Yes. If H₀ is true, P(Type I error) = α. So a test at α = 0.01 has a 1% chance of a false positive, and switching to α = 0.05 raises that chance to 5%.

Does increasing sample size reduce Type I error?

No. P(Type I error) stays at whatever α you choose. A larger sample shrinks the standard error, which lowers P(Type II error) and increases power.

What's the difference between a Type I and Type II error?

A Type I error rejects a true H₀ (a false positive). A Type II error fails to reject a false H₀ (a false negative). If you rejected H₀, only a Type I error is possible. If you failed to reject, only a Type II error is possible.

How do you describe a Type I error in context on the AP Stats FRQ?

State the truth and the wrong conclusion using the problem's parameter. For a test of whether the mean number of bedrooms differs from 2.9, you'd write: "The researcher concludes the mean number of bedrooms in newly built houses differs from 2.9 when it actually is 2.9."