The null hypothesis (H0) is the default claim in a significance test that there is no effect or no difference, like H0: p₁ = p₂ or H0: β = 0. On AP Stats, every p-value is computed assuming H0 is true, and you reject H0 when the p-value is less than or equal to α.
The null hypothesis, written H0, is the skeptic's claim in any significance test. It says nothing interesting is going on. The new drug doesn't work, the two groups have the same proportion, the slope of the regression line is really zero. In CED language, the null hypothesis "specifies a value of 0 for the difference in population proportions, indicating no difference or effect." For a two-proportion test that looks like H0: p₁ = p₂ (equivalently H0: p₁ - p₂ = 0), and for a slope test it's H0: β = β₀, almost always H0: β = 0.
Here's the part that trips people up. You never prove H0 true. The whole logic of a significance test runs the other way. You temporarily assume H0 is true, build the null distribution under that assumption, and then ask how surprising your sample data would be. If the data would be really unlikely under H0 (small p-value), you reject H0 in favor of the alternative. If not, you "fail to reject" H0, which is the statistical version of "not enough evidence to convict," not a declaration of innocence. Two non-negotiables for the exam: H0 is always a statement of equality, and it's always written about population parameters (p, μ, β), never sample statistics (p̂, x̄, b).
The null hypothesis is the backbone of every inference unit in AP Stats, but it's formally pinned down in Topic 6.10 (Setting Up a Test for the Difference of Two Population Proportions) and Topic 9.5 (Carrying Out a Test for the Slope). Learning objective 6.10.A asks you to identify the null and alternative hypotheses, with the CED specifying H0: p₁ = p₂ or H0: p₁ - p₂ = 0. In Unit 9, objectives 9.5.A through 9.5.C all lean on H0. The test statistic t = (b - β)/SE_b is computed using the null value of β, the p-value interpretation must state that you assumed the true population slope equals the value in H0 (that's 9.5.B), and the formal decision in 9.5.C explicitly compares the p-value to α to decide whether to reject H0: β = β₀. If you can't write and interpret a null hypothesis cleanly, every significance test FRQ from Unit 6 through Unit 9 falls apart.
Keep studying AP Statistics Unit 6
Alternative Hypothesis (Ha) (Units 6-9)
H0 and Ha are a matched pair. H0 claims equality (p₁ = p₂), while Ha claims the effect you're actually looking for, either one-sided (p₁ < p₂ or p₁ > p₂) or two-sided (p₁ ≠ p₂). Rejecting H0 is your evidence for Ha. You never gather evidence FOR the null.
Significance Level (α) (Units 6-9)
α is the cutoff that turns a p-value into a decision about H0. The CED rule is mechanical and worth memorizing exactly. If p-value ≤ α, reject H0. If p-value > α, fail to reject H0. No middle ground, no "accept H0."
Hypothesis Test (Units 6-9)
Every hypothesis test in the course, whether it's a one-proportion z-test, two-sample z-test, t-test for means, chi-square test, or t-test for slope, follows the same script. State H0, assume it's true, compute a test statistic and p-value under that assumption, then decide. The null distribution (like the t-distribution with n - 2 df for slopes) only exists because you assumed H0 was true.
Confidence Interval (Units 6-9)
Confidence intervals and tests are two views of the same inference. If a 95% interval for p₁ - p₂ doesn't contain 0, that's consistent with rejecting H0: p₁ - p₂ = 0 at α = 0.05. The null value being inside or outside the interval is a fast mental check on test results.
On multiple choice, expect stems like "Which of the following is the correct null hypothesis?" where wrong answers use sample statistics (p̂₁ = p̂₂) or inequality signs in H0. Also expect p-value interpretation questions, where the credited answer must include the phrase "assuming the null hypothesis is true" (that's the heart of LO 9.5.B). On free response, significance test questions are a four-part template and H0 shows up in three of them. You state hypotheses in correct symbols with parameters defined, you compute the test statistic using the null value, and you write a conclusion that explicitly compares p to α and says "reject H0" or "fail to reject H0" in context. Graders dock you for "accept the null hypothesis," for hypotheses about statistics instead of parameters, and for conclusions that claim H0 is proven true. The two-sample proportion setup (H0: p₁ - p₂ = 0) and the slope test (H0: β = 0, using a t-distribution with n - 2 degrees of freedom) are the two flavors most directly named in Topics 6.10 and 9.5.
H0 is the boring "no effect" claim with an equals sign, and Ha is the research claim with <, >, or ≠. The confusion shows up when writing hypotheses from a word problem. The thing the researcher hopes to show always goes in Ha, never H0. So if a study asks whether a new fertilizer increases yield, H0 says the means are equal and Ha says the fertilizer mean is greater. The test then assumes H0 and looks for evidence toward Ha, which is why you can reject H0 but never prove it.
The null hypothesis is always a statement of equality about population parameters, like H0: p₁ = p₂ or H0: β = 0, never about sample statistics like p̂ or b.
Every p-value is calculated assuming H0 is true, and your interpretation must say so to earn full credit.
The decision rule is exact and mechanical. If the p-value ≤ α, reject H0; if the p-value > α, fail to reject H0.
You never "accept" the null hypothesis. Failing to reject H0 means insufficient evidence against it, not proof that it's true.
For a difference of two proportions (Topic 6.10), the null specifies a difference of 0, which is why you pool the proportions when checking conditions and computing the test statistic.
For a regression slope test (Topic 9.5), assuming H0 is true makes the test statistic t = (b - β)/SE_b follow a t-distribution with n - 2 degrees of freedom.
The null hypothesis (H0) is the default claim of no effect or no difference that a significance test assumes is true. It's written as an equality about a population parameter, such as H0: p₁ = p₂ for two proportions or H0: β = 0 for a regression slope.
No. A large p-value means you fail to reject H0, which only says you lack convincing evidence against it. AP graders specifically penalize "accept H0" because the test was never designed to prove the null true.
H0 uses an equals sign and claims no effect, while Ha uses <, >, or ≠ and states the effect the researcher is trying to find. The test assumes H0 and measures how strongly the data point toward Ha.
Hypotheses are claims about the whole population, which is what you're trying to learn about. The sample statistic (like p̂ or b) is your evidence, so writing H0: p̂₁ = p̂₂ is circular and loses credit on the FRQ.
It's H0: β = β₀, almost always H0: β = 0, meaning there is no linear relationship between the variables in the population. Assuming this null is true, the statistic t = (b - β)/SE_b follows a t-distribution with n - 2 degrees of freedom.
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