Hypothesis Testing – AP Statistics | ShowMeClass

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Hypothesis Testing

AP Statistics · Unit 6: Inference for Categorical Data

Learning Objectives

State H₀ and Hₐ correctly

Compute z-statistic and p-value

Interpret p-value and reach a conclusion

Understand Type I and Type II errors

Key Formulas

Decision Rule

p-value ≤ α: Reject H₀ (statistically significant)

p-value > α: Fail to Reject H₀ (not significant)

"Fail to reject" ≠ "Accept H₀". Never say you "accept" H₀ on the AP exam!

Hypothesisp-valuez-testAP Stats

z-test (proportion)

t-test (mean)

χ²-test (goodness)

Test Statistic

—

p-value

—

α level

0.05

Decision

—

z-test for proportion

H₀: p₀ 0.50

Sample p̂ 0.60

Sample size n 50

t-test for mean

H₀: μ₀ 100

Sample x̄ 104

Sample SD s 10

Sample size n 30

χ²-test

χ² statistic 4.5

Degrees of freedom df 3

Significance α

Alternative Hₐ

📝 Quick Quiz▼

1. A p-value of 0.03 with α = 0.05 means you should:

Fail to reject H₀ Reject H₀ Accept H₀ Accept Hₐ

2. Rejecting H₀ when it is actually true is a:

Type II error Correct decision Type I error Power error

3. The probability of a Type I error equals:

β 1 − β α p-value