Type I error: Rejecting H 0 when it is true. Type II error: Failing to reject H0 when it is false. α=P(type I error) = P(reject H0 when H0 is true) P-value is smallest level of significance that would lead to rejection of H0 . 1) Parameter of interest 2) Null Hypothesis 3) Alternative Hypothesis 4) Test statistic 5) Reject H0 if… 6) Computations 7) Conclusions Inference on the mean of a population, variance known Random sample size n, normally distributed. = -/ Z0 X μ0σ n P-value: ( - ( )) 2 1 ϕ Z0 for two-sided. 1-sided = 1-Φ(Z0 ) when µ > µ o , or Φ(Z0 ) when µ < µ0 . Reject α if z0 is > z α/2 or z0 is < z α/2 and fail to reject if –z α2 <= z0 <= z α/ 2 (two-sided). } Critical For one-sided, reject if z0 > z a (µ > µ0 ), reject if z0 < -z a (µ < µ0 ). } regions! Probability of Type II Error for Two-Sided Alternative Hypothesis on the Mean, Variance Known = -- --β ϕZα2 δnσ ϕ Zα2 δnσ For One-sided: = -β ϕZα δnσ Sample Size for Two-Sided Alternative Hypothesis on the Mean, Variance Known = ( + ) n Zα2 Zβ 2σ2δ2 , where Z β = -(-) Zα2 δnσ and = -δ μ μ0 For One-sided: = ( + ) n Zα Zβ 2σ2δ2 Confidence Interval on the Mean, Variance Known-/ ≤ ≤ + / x zα 2σn μ x zα 2σn Sample Size for a Specified E on the Mean, Variance Known
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