15 flashcard terms for AP Statistics Unit 6, written to match the course framework. Study them here, then drill them as interactive flashcards — free, no account needed.
Range of plausible values for population parameter. 95% CI means: if we repeated sampling infinitely, 95% of intervals contain true μ.
Confidence Level
Probability that confidence interval method produces interval containing parameter. 90%, 95%, 99% common. Higher % = wider interval.
Margin of Error
Half-width of confidence interval; distance from estimate to endpoint. ME = t*·SE. Larger n or lower confidence = smaller ME.
CI for Population Mean (σ known)
x̄ ± z*·(σ/√n) where z* depends on confidence level (1.96 for 95%). Rarely used (σ usually unknown).
CI for Population Mean (σ unknown)
x̄ ± t*·(s/√n) where t* from t-distribution with df=n-1. s = sample standard deviation. Most practical scenario.
Hypothesis Test Setup
H₀ (null): status quo, no effect, parameter = specified value. Hₐ (alternative): claim to test. Test whether data contradicts H₀.
One-tailed vs Two-tailed Tests
One-tailed: Hₐ says > or <. Two-tailed: Hₐ says ≠. Two-tailed more conservative; splits α between tails.
P-value Definition
Probability of observing test statistic as extreme or more extreme assuming H₀ true. Small p-value = strong evidence against H₀.
Significance Level α
Threshold for rejecting H₀; typically 0.05. If p-value < α, reject H₀ (statistically significant result).
Type I Error
Reject H₀ when true (false positive). Probability = α. Example: conclude medicine works when it doesn't.
Type II Error
Fail to reject H₀ when false (false negative). Probability = β. Example: conclude medicine doesn't work when it does.
Power
Power = 1 - β; probability of rejecting false H₀. Higher power = better test. Increases with larger n, larger effect, larger α.
t-test for Population Mean
Test H₀: μ = μ₀. Test statistic: t = (x̄ - μ₀)/(s/√n). Compare to t-distribution with df = n-1.
Assumptions for t-test
Data from random sample, observations independent, population approximately normal (or large n). Robust to normality if n large.
Unit 6 Summary
Confidence intervals estimate parameters with specified confidence. Hypothesis tests assess evidence against null hypothesis using p-values and significance levels.