A Type II error happens when the null hypothesis is actually false but your significance test fails to reject it. In other words, a real effect exists, but your test misses it. It's the false negative of hypothesis testing.
A Type II error is when the null hypothesis is false, but your test fails to reject it (AP Stats 6.7.A). Think of it as a missed catch. There really is an effect or difference out there, but your sample didn't give you enough evidence to spot it, so you stuck with the null.
Quick mental picture: a new drug genuinely works, but your test says "not enough evidence," so you conclude it doesn't. That miss is a Type II error, also called a false negative. The probability of making one is written β (beta), and it's tied directly to power. In fact, the power of a test = 1 − β (AP Stats 6.7.B). A test with low power makes Type II errors easy.
Type II error shows up in Unit 6 (topic 6.7, Potential Errors When Performing Tests) and threads straight into Unit 7's inference for means. Learning objective AP Stats 6.7.A asks you to identify it, 6.7.B asks you to connect its probability to power, 6.7.C asks what factors shrink it, and 6.7.D asks you to interpret it in context. This is one of the most reliably tested ideas in the course because it forces you to think about what a test can get wrong, not just whether you reject. Topic 7.1 frames the whole thing as a question worth worrying about: random variation can lead your conclusions astray, and Type II error is one of two ways that happens.
Keep studying AP Statistics Unit 7
Type I Error (Unit 6)
These two are a matched pair. A Type I error rejects a true null (false positive); a Type II error fails to reject a false null (false negative). Tightening α to avoid a Type I error usually makes a Type II error more likely, so they trade off against each other.
Power of a Test (Unit 6)
Power and Type II error are flip sides of the same coin: power = 1 − β. Anything that raises power (bigger sample, larger α, smaller standard error, a true parameter far from the null) lowers your chance of a Type II error (AP Stats 6.7.C).
Difference of Two Means Tests (Unit 7)
When you run a two-sample t-test (topic 7.9) and fail to reject H₀: μ₁ = μ₂, a Type II error is possible if the means really do differ. The same error idea from Unit 6 carries directly into quantitative inference.
Alpha Level (Unit 6)
Raising α (say from 0.01 to 0.05) makes it easier to reject, which lowers your Type II error rate but raises your Type I error rate. Choosing α is really a decision about which mistake you'd rather avoid.
On multiple choice, you'll see questions that ask you to identify which error is happening or what factor changes its probability. One classic stem describes a quality control engineer switching from α = 0.05 to α = 0.01 and asks about the statistical fallout (lower Type I risk, higher Type II risk). Another asks which question matters most when failing to detect a real treatment effect is the more serious mistake, that's pointing you at Type II error and power. On FRQs, error interpretation shows up in context. The 2018 systolic blood pressure problem (Q6) and the 2021 pet supply repeat-purchase problem (Q4) both involve significance testing where you'd describe what a Type II error would mean for the actual decision. The key skill: don't just name the error, say what it means in the situation ("concluding the treatment doesn't work when it actually does") and which consequence matters more.
A Type I error rejects a null that's actually true (false positive, probability α). A Type II error fails to reject a null that's actually false (false negative, probability β). Easy memory trick: Type I means you cried wolf when there was none; Type II means you missed the wolf that was really there.
A Type II error means the null hypothesis is false but your test fails to reject it, so you miss a real effect (a false negative).
The probability of a Type II error is β, and it relates to power by the rule power = 1 − β.
You lower your Type II error rate by increasing sample size, raising α, decreasing standard error, or having a true parameter farther from the null value.
Type II and Type I errors trade off: shrinking α to avoid false positives makes false negatives more likely.
On FRQs, always interpret the error in context, naming what failing to detect the effect actually means for the decision.
It's when the null hypothesis is actually false, but your significance test fails to reject it, so you miss a real effect. AP Stats 6.7.A calls it a false negative, and its probability is labeled β.
No. A Type I error rejects a true null (false positive, probability α), while a Type II error fails to reject a false null (false negative, probability β). They're opposite mistakes, and reducing one tends to increase the other.
Increase your sample size, raise the significance level α, decrease the standard error, or test when the true parameter is far from the hypothesized value (AP Stats 6.7.C). Each of these also raises the power of the test.
They're complements: power = 1 − β, where β is the probability of a Type II error. A high-power test rarely misses a real effect, so it rarely makes a Type II error.
You won't usually compute β from scratch, but you do need to identify a Type II error, explain what it means in context, and know which factors raise or lower its probability. Connecting it to power (1 − β) is the most commonly tested skill.