AP®︎ Statistics (pre-2026): Unit 6 Flashcards
Master key terms and definitions for Unit 6 of AP Statistics (pre-2026) – Inference for Categorical Data: Proportions to help you prep for quizzes and the AP exam.
Random Variation in Distribution Shape
Differences in sample distribution shape caused by chance rather than an underlying pattern.
Differences in sample distribution shape caused by chance rather than an underlying pattern.
Differences in sample distribution shape caused by bias, error, or real structure in the population.
Ask whether observed differences are due to chance or to a systematic cause.
A symmetric, bell-shaped distribution used to model many sampling distributions and probabilities.
The distribution of sample proportions from many repeated random samples of the same size.
An interval of plausible values for a population proportion based on sample data.
The inference procedure used to estimate one population proportion from one categorical sample.
Check randomization, independence with the 10% condition, and large counts for approximate normality.
Data must come from random selection or random assignment to justify inference assumptions.
When sampling without replacement, the sample size must be no more than 10% of the population.
The proportion of successes in the sample, used as the point estimate of p.
A single sample statistic used to estimate the corresponding population parameter.
The estimated standard deviation of p-hat, equal to sqrt[p-hat(1 minus p-hat)/n].
The z-score cutting off the middle C% of the standard normal distribution.
Construct p-hat plus or minus z-star times sqrt[p-hat(1 minus p-hat)/n].
Solve the margin of error formula for n using a guessed p-hat or 0.5.
Use 0.5 when no estimate is available to get the largest required sample size.
State the confidence interval as a range of plausible population proportions with proper units or labels.
The amount added and subtracted from p-hat, equal to z-star times its standard error.
For one-sample proportion inference, the sample must have at least 10 expected or observed successes and 10 failures: for confidence intervals, n(p-hat) and n(1-p-hat) must both be at least 10; this is also called the success-failure condition.
A specific interval either contains the true population proportion or it does not.
If the claimed proportion is inside the interval, the claim is plausible; if outside, doubt it.
For the same sample data, higher confidence levels produce wider intervals.
The interval's width equals twice the margin of error.
State that you are C% confident the interval contains the true population proportion in context.
In repeated random sampling, about C% of similarly constructed confidence intervals will capture the true population parameter.
Larger samples produce smaller standard errors and therefore narrower confidence intervals; interval width decreases at a rate proportional to 1/sqrt(n).
H0: p = p0; Ha: p < p0, p > p0, or p ≠ p0.
One-sided uses < or >; two-sided uses ≠.
Even for one-sided tests, the null is tested at p = p0.
The hypothesized value usually represents no change, difference, or treatment effect.
Data must come from a random sample or randomized experiment.
When sampling without replacement, check that n ≤ 0.10N to justify independence.
Assuming H0 is true, require np0 ≥ 10 and n(1 - p0) ≥ 10.
The distribution of possible test statistic values when the null hypothesis is assumed true.
A simulated null distribution from repeated randomization versus a model-based z distribution under stated assumptions.
Observed statistic minus null parameter value, divided by the statistic's standard deviation under the null.
Use right-tail area for >, left-tail area for <, and both tails beyond |z| for ≠.
It is computed under the assumption that the null hypothesis and probability model are true.
The standardized difference between p-hat and p0 using sqrt(p0(1-p0)/n).
Small values give strong evidence against the null; large values give weak evidence.
A significance test using a z statistic to compare a sample proportion to a hypothesized population proportion.
Reject means sufficient evidence for Ha; fail to reject means insufficient evidence for Ha.
Not rejecting H0 does not prove it true; it only shows weak evidence against it.
Small values give stronger evidence for Ha; larger values do not support Ha or prove H0.
Large positive or negative z-values correspond to small p-values and possible rejection of H0.
Reject H0 when the p-value is less than or equal to α; otherwise fail to reject H0. If H0 is rejected, the result is statistically significant.
The probability, assuming the null hypothesis is true, of getting the observed result or one more extreme.
Rejecting a true null hypothesis.
Failing to reject a false null hypothesis.
The probability of a Type II error when the null hypothesis is false.
The probability of correctly rejecting a false null hypothesis.
Power = 1 - β, so increasing one decreases the other.
Reject H0 when true: Type I; fail to reject H0 when false: Type II; other outcomes are correct.
Larger samples, larger α, smaller standard error, or a true parameter farther from null.
Choose α based on which mistake is more serious, since α controls Type I error risk.
The chosen cutoff probability for statistical significance; it is also the probability of a Type I error when the null hypothesis is true.
A confidence interval procedure for estimating p1 minus p2 using two independent samples.
The difference between the sample proportions, calculated as p̂1 minus p̂2.
Use (p̂1-p̂2) ± z* times sqrt[p̂1(1-p̂1)/n1 + p̂2(1-p̂2)/n2].
A technology command that computes a confidence interval for p1-p2 from two samples of successes and totals.
Use independent random samples or random assignment, the 10% condition, and large counts in both groups.
The interval’s spread is z* times the standard error from both sample proportions.
In many repeated random samples, about C% of such intervals capture the true difference.
The interval estimates the difference in true population proportions, not the observed sample proportions.
The interpretation must name the populations represented by the samples and the variable being compared.
Check whether the claimed value, usually 0, falls inside the interval.
If 0 is excluded, a difference is supported; the sign shows which proportion is larger.
We are C% confident that the true difference in population proportions, p1 - p2, lies between the interval endpoints, stated in context.
The true population proportions for the two groups being compared.
Requires random samples or random assignment, independent groups, and each sample under 10% of its population.
The combined sample proportion, p-hat-c = (x1 + x2)/(n1 + n2), used in a two-proportion z-test under the null hypothesis that the population proportions are equal.
A significance test comparing two population proportions using a z statistic.
z = (p̂1 - p̂2) divided by the pooled standard error, assuming p1 = p2.
State H0: p1 = p2 or p1 - p2 = 0, versus Ha: p1 < p2, p1 > p2, or p1 ≠ p2, depending on the claim.
The probability, assuming the population proportions are equal, of getting a sample difference at least as extreme as the one observed.
The null hypothesis includes equality, H0: p1 = p2 or p1 - p2 = 0, while the alternative uses <, >, or ≠ to describe the claimed difference.
State the test decision and whether the data provide convincing evidence for the claimed population proportion or difference in proportions, in the context of the problem.
