---
title: "Rejection Region — AP Stats Definition & Exam Guide"
description: "The rejection region is the set of test statistic values that makes you reject H₀, set by the significance level α. See how it links to Type I error and p-values."
canonical: "https://fiveable.me/ap-stats/key-terms/rejection-region"
type: "key-term"
subject: "AP Statistics"
unit: "Unit 7"
---

# Rejection Region — AP Stats Definition & Exam Guide

## Definition

In AP Statistics, the rejection region is the set of test statistic values (in the tails of the sampling distribution) that leads you to reject the null hypothesis; its size is set by the significance level α, and its placement depends on whether the alternative hypothesis is one-sided or two-sided.

## What It Is

The rejection region is the "reject H₀ zone" on the [sampling distribution](/ap-stats/unit-5/central-limit-theorem/study-guide/DPmpebCrsJBYfpSgOKn3 "fv-autolink"). Before you collect data, you pick a [significance level](/ap-stats/key-terms/significance-level "fv-autolink") α (often 0.05). That α carves out an area in the tail (or tails) of the distribution. If your test statistic, like the t-statistic in a one-sample t-test for a mean, lands inside that zone, you reject the null hypothesis. If it lands outside, you fail to reject.

Where the region sits comes straight from your alternative hypothesis ([AP Stats](/ap-stats "fv-autolink") 7.4.B). If Hₐ: μ > μ₀, the rejection region is the right tail. If Hₐ: μ < μ₀, it's the left tail. If Hₐ: μ ≠ μ₀, you split α between both tails. Think of it like a high-jump bar. The significance level sets how high the bar is, and the test statistic either clears it (reject H₀) or doesn't. One thing to know up front is that the AP exam usually frames decisions with p-values instead of rejection regions, but they are two ways of saying the exact same thing. A test statistic falls in the rejection region exactly when the p-value falls below α.

## Why It Matters

Rejection regions live in Topic 7.4, Setting Up a Test for a Population Mean, supporting AP Stats 7.4.A and 7.4.B. When you write H₀: μ = μ₀ and choose a one-sided or two-sided alternative, you're also deciding where the rejection region goes, which changes how extreme your t-statistic has to be. The concept also explains [Type I error](/ap-stats/key-terms/type-i-error "fv-autolink") in a way that finally clicks. The probability your statistic lands in the rejection region when H₀ is actually true is exactly α. That's why α is the Type I error rate, not a coincidence. The same logic runs through every inference procedure in Units 6 through 9, from proportions to [slopes](/ap-stats/unit-9 "fv-autolink"), so understanding it once pays off four times.

## Connections

### [Significance Level (Units 6-7)](/ap-stats/key-terms/significance-level)

The significance level α literally is the [area](/ap-stats/unit-5/normal-distribution-revisited/study-guide/dx4vMcx3WjSw68f1Ov66 "fv-autolink") of the rejection region. Choosing α = 0.05 for a two-sided test means putting 0.025 of area in each tail. Change α and the rejection region grows or shrinks with it.

### [Type I Error (Unit 6)](/ap-stats/key-terms/type-i-error)

A Type I error happens when H₀ is true but your [statistic](/ap-stats/key-terms/statistic "fv-autolink") still lands in the rejection region by random chance. Since that region has area α, the probability of a Type I error is exactly α. The rejection region is the picture behind that fact.

### [Alternative Hypothesis (Units 6-7)](/ap-stats/key-terms/alternative-hypothesis)

The [alternative hypothesis](/ap-stats/key-terms/alternative-hypothesis "fv-autolink") decides placement. Hₐ: μ > μ₀ puts the whole region in the right tail, Hₐ: μ < μ₀ puts it in the left, and Hₐ: μ ≠ μ₀ splits it across both tails. Same α, different geometry.

### [Type II error (Unit 6)](/ap-stats/key-terms/type-ii-error)

If your statistic misses the rejection region when H₀ is actually false, that's a Type II error. Making the rejection region bigger (raising α) lowers the chance of a Type II error but raises the chance of a Type I error, which is the classic tradeoff.

## On the AP Exam

Multiple-choice questions test whether you know which tail(s) the rejection region occupies for a given alternative hypothesis, and whether a given t-statistic or p-value leads to rejecting H₀ at a stated α. For example, a question might give you a t-statistic of 0 from a sample of 15 with Hₐ: μ > μ₀ and ask for the p-value. The answer is 0.5, and rejection-region thinking makes that obvious because t = 0 sits dead center, as far from the tail as possible. On FRQs, the College Board expects the p-value decision rule (reject H₀ if p-value < α), which is logically identical to checking the rejection region. The 2018 FRQ on systolic blood pressure (testing against a reported mean of 122) is the kind of significance-test setup where this decision logic earns points. Just don't mix languages. Compare the p-value to α, or compare the test statistic to the critical value, but not the p-value to the critical value.

## Rejection region vs P-value

These are two routes to the same decision. The rejection region approach fixes a cutoff in advance (a critical value from α) and checks whether your test statistic is beyond it. The p-value approach computes how extreme your statistic actually is and compares that probability to α. Reject with one method and you'd reject with the other, always. The AP exam strongly favors the p-value approach on FRQs, so use rejection regions as intuition and p-values as your written justification.

## Key Takeaways

- The rejection region is the set of test statistic values that leads you to reject the null hypothesis, and its total area equals the significance level α.
- The alternative hypothesis determines placement, with Hₐ: μ > μ₀ using the right tail, Hₐ: μ < μ₀ using the left tail, and Hₐ: μ ≠ μ₀ splitting α between both tails.
- If the null hypothesis is true, the probability your statistic lands in the rejection region anyway is exactly α, which is why α is the Type I error rate.
- A test statistic falls in the rejection region if and only if the p-value is less than α, so the two decision rules always agree.
- On AP FRQs, write your conclusion using the p-value compared to α, and never compare a p-value directly to a critical value.

## FAQs

### What is the rejection region in AP Stats?

It's the range of test statistic values, located in the tail(s) of the sampling distribution, that makes you reject the null hypothesis. Its area equals the significance level α, so with α = 0.05 and a one-sided test, the rejection region is the most extreme 5% of the distribution.

### Is the rejection region the same as the p-value?

No, but they always lead to the same decision. The rejection region is a fixed zone set by α before you see data, while the p-value measures how extreme your actual statistic is. The statistic lands in the rejection region exactly when the p-value drops below α.

### Does the AP Stats exam use rejection regions or p-values?

FRQs expect the p-value approach, where you reject H₀ if the p-value is less than α. Rejection regions are still fair game conceptually in multiple choice, especially questions about one-tailed versus two-tailed tests and Type I error.

### How does a two-tailed test change the rejection region?

A two-sided alternative like Hₐ: μ ≠ μ₀ splits α between both tails, so at α = 0.05 each tail gets area 0.025. That pushes the critical values farther out, meaning your t-statistic must be more extreme to reject than in a one-tailed test at the same α.

### If my test statistic falls in the rejection region, does that prove the null hypothesis is false?

No. It means the data are unlikely if H₀ were true, so you reject H₀, but there's still a probability α that you rejected a true null (a Type I error). Statistical tests give evidence, never proof.

## Related Study Guides

- [7.4 Setting Up a Test for a Population Mean](/ap-stats/unit-7/setting-up-test-for-population-mean/study-guide/1gAGgo2P3abc5G0sLvMr)

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