---
title: "Null Hypothesis — AP Stats Definition & Exam Guide"
description: "The null hypothesis (H₀) is the 'no effect, no difference' claim every significance test assumes true. It drives p-values, Type I errors, and conclusions in Units 6-9."
canonical: "https://fiveable.me/ap-stats/key-terms/null-hypothesis"
type: "key-term"
subject: "AP Statistics"
unit: "Unit 4"
---

# Null Hypothesis — AP Stats Definition & Exam Guide

## Definition

In AP Statistics, the null hypothesis (H₀) is the statement assumed true unless evidence suggests otherwise, always containing an equality (like p = 0.5, μ₁ = μ₂, or β = 0). Every p-value is calculated assuming H₀ is true, and you either reject it or fail to reject it based on the significance level α.

## What It Is

The null hypothesis, written H₀, is the [claim](/ap-stats/unit-3/justifying-claim-based-on-confidence-interval-for-population-proportion/study-guide/YeTpyj6nyq03j0AJO3Bm "fv-autolink") of "no effect, no difference, nothing going on." Per the CED (6.4.A), it's the situation assumed to be correct unless evidence suggests otherwise, while the [alternative hypothesis](/ap-stats/key-terms/alternative-hypothesis "fv-autolink") is the situation you're collecting evidence FOR. The null always contains an equality reference (=, ≥, or ≤) about a population *parameter*, never a sample statistic. So you write H₀: p = 0.40, not H₀: p̂ = 0.40.

Here's the mental model that makes everything in Units 6-9 click. The null hypothesis is like "innocent until proven guilty." You assume H₀ is true, then ask how surprising your sample data would be under that assumption. That [probability](/ap-stats/unit-2/intro-probability/study-guide/gfnBWfyMANOxF3vWLrbA "fv-autolink") is the p-value. If the data would be really rare under H₀ (p-value ≤ α), you reject H₀ in favor of the alternative. If not, you fail to reject H₀. Notice you never "accept" or "prove" the null. A not-guilty verdict doesn't prove innocence; it just means the evidence wasn't strong enough.

## Why It Matters

The null hypothesis is the backbone of all four inference units. It appears in CED learning objectives across proportions ([AP Stats](/ap-stats "fv-autolink") 6.4.A, 6.10.A), means (AP Stats 7.4.B, 7.8.B), [chi-square tests](/ap-stats/key-terms/chi-square-tests "fv-autolink") (AP Stats 8.2.B, 8.5.A), and regression slopes (AP Stats 9.4.B). The form changes by context. For one proportion it's H₀: p = p₀. For two means it's H₀: μ₁ = μ₂. For chi-square independence it's a sentence, "there is no association between the two categorical variables." For slope it's H₀: β = β₀ (usually β = 0, meaning no linear relationship).

It also matters because two other heavily tested ideas are defined entirely in terms of H₀. The [p-value](/ap-stats/key-terms/p-value "fv-autolink") (AP Stats 6.5.B) is computed *assuming the null is true*, and every correct p-value interpretation on the exam must say so. Type I and Type II errors (AP Stats 6.7.A) are literally "rejecting a true null" and "failing to reject a false null." If you're shaky on what H₀ means, those topics fall apart with it.

## Connections

### [Alternative Hypothesis (Units 6-9)](/ap-stats/key-terms/alternative-hypothesis)

H₀ and Hₐ are a matched pair. The null gets the equality (=, ≥, ≤) and the alternative gets the strict inequality (<, >, ≠). The [research question](/ap-stats/unit-3/carrying-out-chi-square-test-for-homogeneity-or-independence/study-guide/AmRuD3egBrZMCLGaBpMw "fv-autolink") lives in Hₐ, but the entire test is run as if H₀ were true.

### [p-value (Unit 6, Topic 6.5)](/ap-stats/key-terms/p-value)

A p-value only means something relative to the null. It's the probability of getting a [test statistic](/ap-stats/key-terms/test-statistic "fv-autolink") as extreme or more extreme than yours, given that H₀ is true. The exam loves penalizing interpretations that skip the "assuming the null is true" part.

### Type I and Type II Errors (Unit 6, Topic 6.7)

Both errors are defined by what you do to the null. Type I rejects a true H₀ (false positive) and happens with probability α. Type II fails to reject a false H₀ (false negative). You can't classify an error on the exam without first stating what H₀ claims.

### [Chi-Square Tests (Unit 8, Topics 8.2 and 8.5)](/ap-stats/key-terms/chi-square-tests)

In Unit 8 the null switches from a symbol to a sentence, like "there is no association between the variables." The null also generates the expected counts (sample size times null proportion), so H₀ isn't just a statement here, it's the calculation engine.

### t-Test for Slope (Unit 9, Topics 9.4-9.5)

H₀: β = 0 says there is no linear relationship between x and y in the population. Rejecting it is how you argue a regression slope is statistically meaningful, which closes the loop back to the scatterplots and LSRLs from Unit 2.

## On the AP Exam

Multiple choice questions test whether you can write the correct H₀ for a scenario (parameter, not statistic, with equality), match a null to the right test, and interpret a p-value or error in terms of H₀. On the free response, the inference FRQ is nearly guaranteed, and stating hypotheses correctly is the first scoring component. Released FRQs show the range. The 2017 exam asked whether age-at-diagnosis data for 207 schizophrenia patients showed a difference between men and women (a chi-square setup where H₀ is "no difference in distributions"). The 2018 exam used mean systolic blood pressure of 122 as a null value for a test about a mean, and the ACL recovery question compared two groups. In every case the rubric expects parameter notation, defined symbols, and a conclusion that says "reject H₀" or "fail to reject H₀" by explicitly comparing the p-value to α, then answers the question in context. Saying "accept the null" costs you credit.

## Null Hypothesis vs Alternative Hypothesis

The null (H₀) is what you assume true by default; the alternative (Hₐ) is what you're gathering evidence for. Students mix up which claim goes where. The tell is the math: H₀ always contains the equality (p = 0.5, μ₁ = μ₂), while Hₐ always contains a strict inequality (<, >, or ≠). The researcher's suspicion or claim of change goes in Hₐ. "No change, no effect, no difference" goes in H₀. Also remember that evidence can support Hₐ (by rejecting H₀), but you never prove H₀.

## Key Takeaways

- The null hypothesis is the default "no effect or no difference" claim, assumed true unless the data provides convincing evidence against it.
- H₀ is always written about a population parameter (p, μ, β) with an equality, never about a sample statistic like p̂ or x̄.
- Every p-value is calculated assuming the null hypothesis is true, and your interpretation must say so to earn full credit.
- You either reject H₀ (when p-value ≤ α) or fail to reject H₀ (when p-value > α). You never "accept" or "prove" the null.
- The null changes form across units: H₀: p₁ = p₂ for two proportions, H₀: μ = μ₀ for a mean, "no association" for chi-square independence, and H₀: β = 0 for regression slope.
- Type I error means rejecting a true null (probability α), and Type II error means failing to reject a false null.

## FAQs

### What is the null hypothesis in AP Stats?

It's the statement assumed true unless evidence suggests otherwise, always claiming no effect or no difference about a population parameter. Examples include H₀: p = 0.5 for a proportion, H₀: μ₁ = μ₂ for two means, and H₀: β = 0 for a regression slope.

### If the p-value is big, do I accept the null hypothesis?

No. When the p-value is greater than α, you "fail to reject H₀," which means there's insufficient evidence for the alternative, not that the null is proven true. Writing "accept the null" on an FRQ loses credit.

### How is the null hypothesis different from the alternative hypothesis?

The null is the default "nothing's going on" claim with an equality (=, ≥, ≤), while the alternative is the claim you're collecting evidence for, with a strict inequality (<, >, or ≠). The test assumes H₀ is true and asks whether the data is surprising enough to support Hₐ.

### Why do you write H₀: p = 0.5 instead of H₀: p̂ = 0.5?

Hypotheses are claims about the population parameter, not the sample. You already know p̂ exactly from your data, so there's nothing to test about it. The unknown population proportion p is what the test is actually about.

### What does the null hypothesis look like for a chi-square test?

It's written in words, not symbols. For goodness of fit, H₀ specifies the null proportions for each category. For independence, H₀ says there is no association between the two categorical variables. For homogeneity, H₀ says there is no difference in distributions across populations or treatments.

## Related Study Guides

- [4.4 Setting Up a Test for a Population Mean or Population Mean Difference](/ap-stats/unit-4/setting-up-test-for-population-mean/study-guide/1gAGgo2P3abc5G0sLvMr)
- [Legacy AP Statistics Topic: Chi-Square Goodness of Fit Setup](/ap-stats/unit-XXGRYZTH6sTfEcdI/setting-up-chi-square-goodness-fit-test/study-guide/2W5HT2MbSAG4Ty1buvCd)
- [Legacy AP Statistics Unit Overview: Means](/ap-stats/unit-kieImJKumIjyX99J/review/study-guide/J8njHeY1jq4jDOeZdjRW)
- [Legacy AP Statistics Topic: Test Setup for Regression Slope](/ap-stats/unit-CL5B675bCTuba5g2/setting-up-test-for-slope-regression-model/study-guide/KEnR8FNAnXWsr8dFSAKG)
- [What Are the Best Quizlet Decks for AP Statistics?](/ap-stats/faqs/quizlet-decks-ap-statistics/study-guide/McK83yVXqkQ58roeeMKG)
- [Legacy AP Statistics Topic: Test Execution for Regression Slope](/ap-stats/unit-CL5B675bCTuba5g2/carrying-out-test-for-slope-regression-model/study-guide/NZoM7ZudTv9aH60Y5hn8)
- [3.7 Carrying Out a Test for a Population Proportion](/ap-stats/unit-3/concluding-test-for-population-proportion/study-guide/THZeUpkm11DAwnNb6p4g)
- [3.10 Constructing a Confidence Interval for the Difference Between Two Population Proportions](/ap-stats/unit-3/confidence-intervals-for-difference-two-proportions/study-guide/YjPeyk5dGYBwzENoOU6S)
- [3.8 Potential Errors When Performing Tests](/ap-stats/unit-3/potential-errors-when-performing-tests/study-guide/YxhrmoLje3YYOwcocJrS)
- [3.6 p-Values](/ap-stats/unit-3/interpreting-p-values/study-guide/b0FEXf5MDjyQtz4Skz70)

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