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L24 - Testing a Normal Mean Earlier found sample size to...

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Unformatted text preview: Testing a Normal Mean Earlier found sample size to achieve specified Type I error α and Type II error β at particular value of alternative parameter. Here n given. Can’t pick it. Stuck with whatever β emerges. Test at the level of significance α H : μ = μ H 1 : μ < μ 1 Recall CR given by { ¯ x < c } , c determined by c- 30 σ/ √ n =- z α that is c = μ- z α σ √ n Decision: Reject H if ¯ X < c. Meaning: Sample average must be a certain number of stan- dard error units away from the null value (similar to being guilty beyond a reasonable doubt in a criminal trial.) 2 Equivalently compute standard- ized z score or signal to noise ratio z = ¯ x- μ σ/ √ n Reject H if z < z α . Note . Can replace H : μ = μ with composite null hypothesis H : μ ≥ μ because from OC curves of previous lec- ture, largest Type I error occurs at boundary between H , H 1 . 3 Example . Data 40 26 39 14 42 18 25 43 46 27 19 47 19 26 35 34 15 44 40 38 31 46 52 25 35 35 33 29 34 41 49 28 52...
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L24 - Testing a Normal Mean Earlier found sample size to...

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