What you'll learn
Drawing conclusions about population proportions (~12–15%).
Confidence intervals
statistic ± (critical value)(standard error). For one proportion: p̂ ± z*√(p̂(1−p̂)/n).
- Interpret: 'We are C% confident the interval captures the true proportion.'
- C% confidence = the method captures the parameter C% of the time (not a probability for one interval).
Significance tests
- Hypotheses: H₀ (e.g. p = p₀) vs Hₐ.
- Conditions: random, 10% (independence), large counts (np₀ ≥ 10, n(1−p₀) ≥ 10).
- Test statistic z and p-value.
- Conclusion: if p-value < α, reject H₀ (evidence for Hₐ); otherwise fail to reject. Always state in context.
Two proportions
Compare p̂₁ − p̂₂ (use a pooled proportion for the test).
Errors & power
- Type I: reject a true H₀ (probability α). Type II: fail to reject a false H₀ (β).
- Power = 1 − β; increases with larger n, larger effect, larger α.
Exam tips
- State and check conditions every time; interpret intervals/p-values in context.
Common mistakes
- Saying 'there's a C% chance the parameter is in the interval.'
- Accepting H₀ (you 'fail to reject', never prove it).