6.4 Setting Up a Test for a Population Proportion (AP Statistics)

What Students Will Learn

• What a hypothesis test for a proportion is and when to use it
• How to correctly define:
  ✔ Population proportion §
  ✔ Sample proportion (p̂)
  ✔ Hypothesized value (p₀)
• How to identify and use a one-sample z-test for proportions
• The meaning of the p-value and how it is interpreted
• How to set up hypotheses correctly:
  ✔ H₀: p = p₀
  ✔ Hₐ: p > p₀, p < p₀, or p ≠ p₀
• How to determine the correct direction of the test
• How to check all required conditions:
  ✔ Random
  ✔ Independence (10% condition)
  ✔ Normality (np₀ ≥ 10 and n(1 − p₀) ≥ 10)

Topics Covered

• One-sample z-test for proportions
• Understanding p-values
• Setting up null and alternative hypotheses
• Right-tailed, left-tailed, and two-tailed tests
• Conditions for valid inference
• Step-by-step test setup process
• Fully worked examples
• Common mistakes and exam traps