AP Statistics — Inference flashcards

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AP Statistics inference, tagged to the Course and Exam Description effective Fall 2026: intervals and tests for proportions and means, chi-square tests, conditions, interpretations, errors and power, and choosing a procedure. Goodness-of-fit and slope-inference cards are marked as background.

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Learn deck · part of AP Statistics · written against: College Board AP Statistics Course and Exam Description effective Fall 2026 (five units; first exam May 2027); cards on topics it removed or does not name are kept as background and say so. Updated 2026-10-10.

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What is the formula for a one-sample z interval for a population proportion?

$\hat{p} \pm z^*\sqrt{\frac{\hat{p}\left(1 - \hat{p}\right)}{n}}$ — the point estimate plus or minus the margin of error.
Inference for Categorical Data Proportions › Constructing a Confidence Interval for a Population Proportion
Which three conditions must you check before building a confidence interval for a proportion?

Random (a random sample), 10% (n under 10% of the population when sampling without replacement), and Large Counts ( $n\hat{p} \ge 10$ and $n\left(1 - \hat{p}\right) \ge 10$ ⁠).
Inference for Categorical Data Proportions › Constructing a Confidence Interval for a Population Proportion
How do you interpret a 95% confidence interval of (0.42, 0.50) for the proportion of voters who support a measure?

We are 95% confident that the interval from 0.42 to 0.50 captures the true proportion of all voters who support the measure. Always name the parameter in context.
Inference for Categorical Data Proportions › Justifying a Claim Based on a Confidence Interval for a Population Proportion
Why do inference procedures for a mean use $t$ rather than $z$ ⁠?

The population SD $\sigma$ is almost never known, so it is estimated by $s$ ⁠, adding variability; the t distributions, with heavier tails, account for it.
Inference for Quantitative Data Means › Constructing a Confidence Interval for a Population Mean or Population Mean Difference
How does a t distribution change as the degrees of freedom increase?

It gets closer to the standard normal — tails become thinner and t* shrinks toward z*.
Inference for Quantitative Data Means › Constructing a Confidence Interval for a Population Mean or Population Mean Difference
What changes in the conclusion when data come from a randomized experiment rather than a random sample?

Random assignment lets you conclude that the treatment caused the difference; random sampling lets you generalize to the population. The 10% condition does not apply to random assignment.
Exploring One-Variable Data and Collecting Data › Data Collection and Random Sampling
What population model underlies inference for a regression slope?

$\mu_y = \alpha + \beta x$ ⁠: the mean response is a linear function of x, and responses vary normally around that line with the same SD $\sigma$ for every x. Beyond the AP course; background only.
Regression Analysis › Least-Squares Regression
What conditions are checked for inference about a regression slope?

Linear relationship, Independent observations (10% condition), Normal residuals, Equal SD (no fanning in the residual plot), Random sample or assignment. Mnemonic: LINER. Beyond the AP course; background only.
Regression Analysis › Linear Regression Models and Residuals
What three questions sort out which inference procedure to use?

Is the response categorical or quantitative? How many samples or groups, and are they paired? Are you estimating (interval) or testing a claim (test)?
Exploring One-Variable Data and Collecting Data › Data Collection and Random Sampling
Why does a matched-pairs design usually give a more powerful test than two independent groups?

Analyzing within-pair differences removes the variation between subjects, so the standard error is smaller and real treatment effects are easier to detect.
Exploring One-Variable Data and Collecting Data › Experimental Design

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Topic outline follows the College Board AP Statistics Course and Exam Description effective Fall 2026 (first exam May 2027); cards on topics that course removed are kept as background and say so. The AP name is used nominatively and no course or exam text is reproduced.
OpenStax Introductory Statistics 2e, consulted as a reference; no text copied.

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