Statistical Inference: Hypothesis Testing for Means and Proportions, Study notes of Statistics

Download Statistical Inference: Hypothesis Testing for Means and Proportions and more Study notes Statistics in PDF only on Docsity! STAT 301 TA : Lisa Chung lchung@stat.wisc.edu DISCUSSION 9 (Mar. 28. 2004) • Test for mean when σ is known or large sample Z = barX−µ0 σ/ √ (n) (1 − α)100% Acceptance Region 1. H0 : µ = µ0 vs.HA : µ 6= µ0 (µ0 − zα 2 σ√ n , µ0 + zα 2 σ√ n ) 2. H0 : µ = µ0 vs. HA : µ > µ0 (−∞, µ0 + zα σ√ n ) 3. H0 : µ = µ0 vs.HA : µ < µ0 (µ0 − zα σ√ n , ∞) • Test for mean with unknown σ and small sample T= X̄−µ s/ √ n ∼ tn−1 If it’s reasonable to assume that the population is normal, then for small n, a 100(1-α)% confidence interval for µ is: (X̄ − tα 2 ,n−1 s√ n , X̄ + tα 2 ,n−1 s√ n ) with degree of freedom n − 1. • Proportion X has a binomial distribution: X ∼ Bin(n, p) , where p is unknown. Let x be the observed value of X, and use the number x to make an inference about the unknown value of p. Point estimate is p̂ = x n The confidence interval for π is (π̂ − zα/2 √ π̂(1 − π̂) n , π̂ + zα/2 √ π̂(1 − π̂) n ) Office: 1335 MSC, 263-5948 1 Office Hour: Wed.1:00-2:00 and Thurs. 11:00-12:00