Read the notes, then try the practice. It adapts as you go.When you're ready.
Session Length
~19 min
Adaptive Checks
17 questions
Transfer Probes
9
Statistical inference is the process of drawing conclusions about populations based on sample data. This topic covers the core inference procedures tested on the AP Statistics exam: sampling distributions, confidence intervals for proportions and means, hypothesis testing using z-tests and t-tests, chi-square tests for categorical data, and inference for regression slopes.
Understanding when and how to apply each procedure, checking conditions, and interpreting results in context are essential skills for the AP exam and for real-world data analysis.
One step at a time.
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The distribution of a statistic computed from all possible samples of a given size. The CLT describes how sampling distributions become approximately normal as sample size increases.
Example: Taking 1000 samples of size 50 and computing each mean yields a bell-shaped histogram centered at the population mean.
For large samples, the sampling distribution of the sample mean is approximately normal regardless of population shape. For proportions, np >= 10 and n(1-p) >= 10 must hold.
Example: Even if a population is right-skewed, sample means from n=40 will be approximately normal.
Interval estimate: p-hat +/- z* sqrt(p-hat(1-p-hat)/n). Conditions: random, Large Counts, 10% condition.
Example: A poll of 400 voters with 55% favoring gives 95% CI = (0.501, 0.599).
Interval estimate using t-distribution: x-bar +/- t* (s/sqrt(n)) with df = n-1. Used when population SD is unknown.
Example: Sample of 25 scores, mean 78, SD 10: 95% CI = (73.87, 82.13).
Formal procedure: state H0 and Ha, compute test statistic, find p-value, conclude in context.
Example: Testing if coin is fair: H0: p=0.5. 62 heads in 100 flips. z=2.4, p=0.016. Reject H0.
Test for categorical data. GOF checks observed vs expected frequencies. Independence checks association between variables. Statistic: sum((O-E)^2/E).
Example: Testing die fairness with observed {15,20,18,12,22,13} vs expected 16.67 each.
Testing whether slope beta = 0. Uses t = b/SE_b with df = n-2. CI: b +/- t* SE_b.
Example: Slope b=3.2, SE=0.8, n=30: t=4.0 with df=28, strong evidence of linear relationship.
Probability of correctly rejecting a false H0: Power = 1 - beta. Increases with larger n, larger effect, higher alpha.
Example: Power of 0.80 means 20% chance of missing a real effect.
Choose a different way to engage with this topic — no grading, just richer thinking.
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See how the key ideas connect. Nodes color in as you practice.
Walk through a solved problem step-by-step. Try predicting each step before revealing it.
This is guided practice, not just a quiz. Hints and pacing adjust in real time.
Small steps add up.
What you get while practicing:
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