Statistical Inference Flashcards

Grade 12 · Math · Flashcards

Master the vocabulary, formulas, and logic of hypothesis testing and confidence interval construction.

Flashcards

Null Hypothesis (H₀): The claim of no effect or no difference; assumed true until evidence shows otherwise
Alternative Hypothesis (H₁): The claim the researcher is trying to find evidence for; accepted when H₀ is rejected
P-Value: P(observing result this extreme | H₀ is true); reject H₀ when p < α
Significance Level α: The threshold for rejecting H₀; equals the probability of committing a Type I error
Type I Error (α): Rejecting a true H₀; false positive
Type II Error (β): Failing to reject a false H₀; false negative
Statistical Power: 1 - β; probability of correctly detecting a true effect; increased by larger n or larger α
Z-Test Formula: z = (x̄ - μ₀) / (σ/√n); use when σ known or n ≥ 30
T-Test Formula: t = (x̄ - μ₀) / (s/√n) with df = n - 1; use when σ unknown
95% CI Formula: x̄ ± 1.96 · (σ/√n) for large samples; uses z* = 1.96
Central Limit Theorem: For large n: x̄ ~ N(μ, σ²/n). Allows normal inference for any population shape
Standard Error: σ/√n (or s/√n); the standard deviation of the sampling distribution of x̄
Margin of Error: z*(σ/√n); determines half-width of confidence interval; decreases as n increases
Chi-Square Test: Tests independence or goodness of fit using categorical data; test statistic χ² = Σ(O-E)²/E