In AP Statistics, the power of a test is the probability that a significance test correctly rejects a false null hypothesis, so power = 1 − β, where β is the probability of a Type II error. Power increases with larger sample size, larger α, smaller standard error, and a true parameter farther from the null.
Power is your test's ability to catch a real effect. If the null hypothesis is actually false, power is the probability your test notices and rejects it. Think of it like a smoke detector. A high-power test is a sensitive detector that goes off when there's a real fire. A low-power test sleeps through the smoke. That "sleeping through it" outcome is a Type II error (failing to reject a false null), which is why the CED gives you the cleanest relationship in the whole unit: power = 1 − β, where β is the probability of a Type II error.
The CED (learning objective 6.7.C) lists exactly four things that increase power, holding everything else constant. Power goes up when (1) sample size increases, (2) the significance level α increases, (3) the standard error decreases, or (4) the true parameter value is farther from the null value. The intuition behind all four is the same. Anything that makes a real difference easier to see (more data, less noise, a bigger gap, or a lower bar for rejecting) makes the test more likely to detect it.
Power lives in Topic 6.7 (Potential Errors When Performing Tests) and gets revisited in Topic 7.1 when inference shifts from proportions to means. It directly supports learning objectives 6.7.B (the power of a test is the probability that a test will correctly reject a false null hypothesis, and P(Type II error) = 1 − power), 6.7.C (factors that affect error probabilities), and 7.1.A (questions suggested by probabilities of errors). It also connects to 6.7.D, because raising α to gain power means accepting more Type I error risk, and which error is worse depends on the situation. This is one of the most reliably tested conceptual ideas in Units 6 and 7 because you can't calculate your way through it. You have to actually understand what rejecting a false null means.
Keep studying AP Statistics Unit 6
Type II Error (Unit 6)
Power and Type II error are two sides of the same coin. When the null is false, the test either rejects it (that probability is the power) or fails to reject it (that probability is β). They must add to 1, so anything that decreases β increases power by exactly the same amount.
Significance Level (Unit 6)
Raising α makes rejecting easier, which raises power but also raises the chance of a Type I error. This is the trade-off at the heart of Topic 6.7. You can't crank up sensitivity to real effects without also getting more false alarms, unless you change something else like sample size.
Sample Size and Standard Error (Unit 7)
Bigger samples shrink the standard error, which tightens the sampling distribution and makes a real difference stand out from random noise. This is the one way to boost power without paying for it in Type I error risk, which is why exam answers about increasing power so often come down to "collect more data."
Hypothesis Test logic (Units 6-7)
Power only makes sense inside the reject/fail-to-reject framework. It assumes a specific world where the null is false and asks how often your test gets it right in that world. That conditional thinking (given the null is false, what happens?) is the same skill you use to interpret p-values and α.
Power shows up almost entirely in multiple choice and in the reasoning parts of inference FRQs, not as a calculation you grind through. Three formats dominate. First, the direct conversion question, like a stem giving you β = 0.25 and asking for the power (it's 0.75, since power = 1 − β). Second, the "which change increases power?" question, where you pick from the four factors in 6.7.C, such as increasing n or increasing α. Third, the trade-off scenario, like a medical researcher or aircraft quality-control engineer choosing a significance level, where you have to weigh the consequences of a false positive against a false negative. On FRQs, expect prompts asking how to increase the power of a described test or which error is more consequential in context. Always answer in context, and never say a test "proves" anything.
Both are probabilities of rejecting the null, but they assume opposite worlds. α is the probability of rejecting when the null is TRUE (a Type I error, a false alarm). Power is the probability of rejecting when the null is FALSE (a correct detection). You choose α before the test; power is a consequence of α, sample size, variability, and how far the truth sits from the null.
Power is the probability that a test correctly rejects a false null hypothesis, and it always equals 1 − β, where β is the probability of a Type II error.
Power increases when sample size increases, when α increases, when standard error decreases, or when the true parameter value is farther from the null (each holding the others constant).
Raising α buys you more power but at the cost of a higher Type I error rate; increasing sample size raises power without that cost.
Power is conditional on the null being false, while α is conditional on the null being true, so they describe rejection probabilities in two different worlds.
On the exam, if a question gives you β, subtract it from 1 to get power, and if it asks how to increase power, the safest answer is usually a larger sample size.
Power is the probability that a significance test correctly rejects a false null hypothesis. It equals 1 − β, where β is the probability of a Type II error, so a test with β = 0.25 has power 0.75.
No. The significance level α is the probability of rejecting the null when it's actually true (a Type I error). Power is the probability of rejecting the null when it's actually false. Same action, opposite assumed realities.
The CED lists four ways: increase the sample size, increase the significance level α, decrease the standard error, or have a true parameter value farther from the null. Increasing sample size is the only one of these you control that doesn't raise Type I error risk.
Increasing α increases power, because a higher α makes it easier to reject the null hypothesis. The catch is that it also increases the probability of a Type I error, so there's a real trade-off.
Not from scratch. The AP exam tests the relationship power = 1 − β, the four factors that affect power, and the α-versus-power trade-off conceptually. Full power calculations from a specific alternative value are beyond the AP curriculum.