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.
The null hypothesis, written H₀, is the claim 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 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 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.
The null hypothesis is the backbone of all four inference units. It appears in CED learning objectives across proportions (AP Stats 6.4.A, 6.10.A), means (AP Stats 7.4.B, 7.8.B), chi-square tests (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 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.
Keep studying AP Statistics Unit 7
Alternative Hypothesis (Units 6-9)
H₀ and Hₐ are a matched pair. The null gets the equality (=, ≥, ≤) and the alternative gets the strict inequality (<, >, ≠). The research question lives in Hₐ, but the entire test is run as if H₀ were true.
p-value (Unit 6, Topic 6.5)
A p-value only means something relative to the null. It's the probability of getting a test statistic 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)
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.
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.
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.
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.
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.
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.
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.
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.
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.