AP®︎ Statistics (pre-2026): Unit 7 Flashcards
Master key terms and definitions for Unit 7 of AP Statistics (pre-2026) – Inference for Quantitative Data: Means to help you prep for quizzes and the AP exam.
Statistical Inference
Using sample data to draw conclusions about a population, with uncertainty from random variation.
Using sample data to draw conclusions about a population, with uncertainty from random variation.
Natural sample-to-sample differences caused by chance rather than a systematic influence.
The difference between a sample result and the true population value caused by random sampling.
Inaccuracy in recorded data because the measuring process or instrument does not capture values exactly.
A systematic error that consistently pushes results away from the true population value.
Type I rejects a true null; Type II fails to reject a false null.
The probability that a test correctly rejects a false null hypothesis.
Lower alpha reduces Type I but raises Type II; larger samples usually reduce Type II and increase power.
A sample chosen so every possible group of the same size has an equal chance.
Volunteer samples use self-selected participants; convenience samples use easily reached participants, often causing bias.
Bias caused when question wording or survey conditions influence how people answer.
A variable related to both explanatory and response variables that distorts their apparent relationship.
Grouping similar experimental units before treatment assignment to control a known source of variation.
A claim about a population parameter that represents no effect or no difference.
The chosen cutoff probability, denoted by α, for rejecting the null hypothesis; it is the probability of rejecting a true null hypothesis.
The number of independent values that can vary after estimating a parameter; for one sample, n - 1.
A mean interval found by analyzing pairwise differences as one sample of differences.
The sample mean x̄, used as the center of the confidence interval.
A bell-shaped distribution with heavier tails than normal that approaches normal as df increases.
Use this method when data are random, independent, and the sample distribution is approximately normal.
The long-run percent of intervals from this method that capture the true mean.
The confidence interval procedure for estimating a population mean when σ is unknown: x̄ ± t*(s/√n).
For estimating a population mean with unknown σ, use x̄ ± t*(s/√n).
State the confidence level, parameter, population, and that the interval came from a sample.
An interval estimating the population mean of pairwise differences from dependent observations.
Higher confidence levels produce wider intervals for the same sample data.
A claimed mean is supported if inside the interval and not supported if outside.
For one mean, larger samples give narrower intervals because width is proportional to 1/√n.
We are C% confident that the true population mean lies between the interval endpoints.
The cutoff value from the t-distribution based on the chosen confidence level and degrees of freedom.
The distance from the sample mean to either endpoint of a confidence interval, equal to the critical value times the standard error.
For a one-sample t procedure, including matched pairs using differences, the degrees of freedom are n - 1.
Treat paired data as one sample of differences, then test the mean difference.
Use H0: μd = 0 or stated value and Ha about μd after defining differences.
Define differences consistently, such as before minus after, so μd has clear meaning.
Check randomization, independence with the 10% condition, and an approximately normal distribution.
State hypotheses about the population mean: the null includes equality, typically H0: μ = μ0, and the alternative is μ < μ0, μ > μ0, or μ ≠ μ0.
A significance test for whether a population mean differs from a hypothesized value when σ is unknown.
t = (x̄ - μ0)/(s/√n), comparing the sample mean to the null mean in standard-error units.
t = (d̄ - μd0)/(sd/√n), using the sample mean and standard deviation of differences.
When sampling from a normal population, the statistic follows a t-distribution with n - 1 degrees of freedom.
Use one tail for directional alternatives and two tails for non-directional alternatives.
State whether the data give convincing evidence for the alternative claim about the population mean.
Match the test statistic with df = n - 1 and read the tail probability; double it for two-sided tests.
Report the test statistic, p-value, and degrees of freedom from technology when performing the test.
The estimated standard deviation of the sampling distribution of the sample mean, calculated as s/√n.
An interval estimate for μ1 - μ2 using x̄1 - x̄2 and a two-sample t procedure.
Parameter: μ1 - μ2; point estimate: x̄1 - x̄2.
Has mean μ1 - μ2 and, when conditions hold, is approximately normal.
Population SD is √(σ1²/n1 + σ2²/n2); estimated SE is √(s1²/n1 + s2²/n2).
Critical value times the standard error: t*√(s1²/n1 + s2²/n2).
(x̄1 - x̄2) ± t*√(s1²/n1 + s2²/n2).
Use the t-distribution critical value for the chosen confidence level with appropriate technology-based degrees of freedom.
Treat the two population variances as unknown and not assumed equal.
Use the two-sample t-interval command to enter sample statistics or data and compute the interval.
Use two independent random samples or random assignment, check 10% when sampling, and verify approximate normality.
We are C% confident that the interval captures the true difference between the two population means, μ1 - μ2, in context.
In repeated random sampling, about C% of such intervals would capture the true population mean difference.
An interpretation must name the samples and the populations they represent in the problem setting.
The default claim is that the true population mean difference equals 0.
Holding other factors constant, larger sample sizes produce narrower intervals for the population mean difference.
A claim is supported when its stated difference is inside the interval, including 0 for no difference.
μ1 and μ2 represent the true population means for groups 1 and 2.
The two samples come from separate groups, so observations in one sample do not affect the other.
Data should come from simple random samples or a randomized experiment.
When sampling without replacement, check that n1 ≤ 10% of N1 and n2 ≤ 10% of N2.
If either sample distribution is skewed, both sample sizes should be greater than 30.
If a sample size is under 30, both samples should show no strong skewness or outliers.
The distribution of x̄1 − x̄2 must be approximately normal for valid inference.
A significance test for comparing the means of two independent groups using sample means and estimated standard errors.
For comparing two population means, the null states no difference, H0: μ1 - μ2 = 0 (or μ1 = μ2), and the alternative states μ1 - μ2 ≠ 0, < 0, or > 0.
(x̄1 - x̄2 - 0) divided by the square root of s1^2/n1 + s2^2/n2.
The estimated spread of x̄1 - x̄2, computed as the square root of s1^2/n1 + s2^2/n2.
A technology-based value between the smaller of n1 - 1 and n2 - 1 and n1 + n2 - 2.
The probability, assuming equal population means, of getting a result at least as extreme.
State whether the data give convincing evidence about a difference in population means in context.
Calculator or software output provides the test statistic, degrees of freedom, and p-value.
Choose by data type, sample count, and whether samples are independent or paired.
Use t procedures for means and z procedures for proportions.
Use one-sample methods for one population and two-sample methods for comparing two populations.
Compares observed and expected counts for categorical data across multiple groups.
State, Plan, Do, Conclude: the standard structure for writing inference free-response answers.
Identify the population parameter and, for tests, write null and alternative hypotheses.
Check inference conditions: random, independent, and normal, in context of the procedure.
Name the procedure and report calculator output such as interval, p-value, df, or test statistic.
State the p-value decision and whether the data give convincing evidence in context.
A t-test on the mean of pairwise differences from dependent observations, such as matched subjects or the same subjects measured twice.
The probability, assuming the null hypothesis is true, of getting the observed result or one more extreme.
Compare the p-value to α: reject H0 if p-value is less than or equal to α; otherwise fail to reject H0.
