In AP Statistics, the alternative hypothesis (Hₐ) is the claim a significance test collects evidence FOR, stating that an effect, difference, or relationship exists. It always uses a strict inequality (<, >, or ≠) about a population parameter, while the null hypothesis uses equality.
The alternative hypothesis (written Hₐ or H₁) is the statement you're trying to find evidence for in a significance test. The null hypothesis (H₀) says "nothing's going on" (no effect, no difference, no relationship), and the alternative says "actually, something IS going on." Per the CED (6.4.A), the null is what we assume is true unless evidence suggests otherwise, and the alternative is the situation for which evidence is being collected.
The alternative always contains a strict inequality about a parameter. If it uses < or >, it's one-sided (you only care about one direction, like "the new drug lowers blood pressure"). If it uses ≠, it's two-sided (any difference matters, in either direction). Which one you pick comes straight from the wording of the research question, not from the data. One critical rule that costs points every year: hypotheses are always about population parameters (p, μ, β, p₁ - p₂), never about sample statistics (p̂, x̄, b). Writing Hₐ: x̄ > 50 is automatically wrong.
The alternative hypothesis is one of the few concepts that shows up in four straight units. You write it for proportions (6.4.A, 6.10.A), means and matched pairs (7.4.B), chi-square tests (8.5.A), and regression slopes (9.4.B). Every significance test FRQ starts the same way, with stating H₀ and Hₐ correctly in context, and that's usually the first scoring component. The alternative also drives interpretation. The p-value measures evidence against H₀ in the direction of Hₐ, so a one-sided alternative gives a different p-value than a two-sided one for the same data. And when you reject H₀, your conclusion is phrased as "convincing evidence for Hₐ" in context. Get the alternative wrong at the start and the whole test unravels.
Keep studying AP Statistics Unit 7
Null Hypothesis (Units 6-9)
These two are a matched pair. The null gets the equality (H₀: p = 0.5) and is assumed true for all calculations; the alternative gets the strict inequality and is what you're hoping the data supports. You never "accept" the null, you either reject it in favor of Hₐ or fail to reject it.
P-value (Units 6-9)
The direction of your alternative determines how the p-value is computed. A one-sided Hₐ counts probability in one tail; a two-sided Hₐ counts both tails, which roughly doubles the p-value. That's why the same regression data can give p = 0.15 for Hₐ: β ≠ 0 but p = 0.075 for Hₐ: β > 0.
Type I and Type II Errors (Unit 6)
Errors are defined by the tug-of-war between H₀ and Hₐ. A Type II error means Hₐ was actually true but your test failed to detect it. Power, the probability of correctly rejecting a false null, goes up when the true parameter is farther from the null value, meaning the alternative is "more true."
Chi-Square Hypotheses (Unit 8)
Chi-square is the one place the alternative is written in words, not symbols. For homogeneity, Hₐ says the distributions of a categorical variable differ across populations; for independence, Hₐ says the two variables are associated. There's no one-sided version because chi-square only detects "different," not a direction.
Stating hypotheses is step one of nearly every significance test FRQ, and the alternative is graded on three things: correct parameter (population, not sample), correct inequality direction matching the question, and context. The 2017 FRQ on schizophrenia diagnosis age and the 2018 FRQ on systolic blood pressure both required correctly set-up hypotheses before any calculation earned credit. Multiple-choice questions test whether you understand what Hₐ does to the test. A common stem gives the same data tested with Hₐ: β ≠ 0 versus Hₐ: β > 0 and asks why the p-values differ (the two-sided p-value is double the one-sided one). Another favorite checks that you know the p-value is computed assuming H₀ is true, not Hₐ. Watch the question wording: "is the mean different from 122" means ≠, while "is the mean greater than 122" means >.
The null hypothesis (H₀) is the boring default you assume true, and it always contains equality (like H₀: μ = 122 or H₀: β = 0). The alternative (Hₐ) is the interesting claim you want evidence for, and it always uses a strict inequality (<, >, or ≠). All test calculations, including the p-value, are done assuming H₀ is true. The data never "proves" Hₐ; a small p-value just gives convincing evidence for it. A handy check: the researcher's question almost always lives in the alternative.
The alternative hypothesis (Hₐ) is the claim you're collecting evidence for, while the null (H₀) is the default you assume true until the data says otherwise.
Hₐ always uses a strict inequality: < or > makes it one-sided, and ≠ makes it two-sided, with the choice determined by the research question's wording.
Hypotheses are always written about population parameters like p, μ, or β, never sample statistics like p̂ or x̄.
A two-sided alternative produces a p-value roughly twice as large as the one-sided version for the same data, because probability is counted in both tails.
For chi-square tests, the alternative is stated in words: the distributions differ (homogeneity) or the variables are associated (independence).
When the p-value ≤ α, you reject H₀ and conclude there is convincing evidence for the alternative hypothesis in context; you never say the data 'proves' Hₐ.
It's the claim a significance test collects evidence for, written Hₐ with a strict inequality about a population parameter, like Hₐ: p > 0.5 or Hₐ: μ ≠ 122. It states that an effect, difference, or relationship actually exists.
No. Rejecting H₀ means the data provide convincing evidence for Hₐ at your significance level, but you could still be making a Type I error (false positive), which happens with probability α when H₀ is true. AP graders penalize the word "prove."
The null contains an equality (H₀: μ = μ₀) and is assumed true for all calculations, while the alternative contains a strict inequality (Hₐ: μ <, >, or ≠ μ₀) and represents the claim being tested. The p-value is always computed assuming the null, not the alternative.
Read the question. "Greater than," "increased," or "improved" means one-sided (> or <); "different from" or "changed" means two-sided (≠). For the same data, the two-sided p-value is about double the one-sided one, so this choice can flip your conclusion.
It's written in words, not symbols. For homogeneity, Hₐ is "there is a difference in the distributions of the categorical variable across populations or treatments"; for independence, Hₐ is "the two categorical variables are associated." Chi-square alternatives are never one-sided.