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post5 - Null(H0 default state we tend to believe it unless...

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Hypothesis Testing Statistical Hypotheses: assertions about the distribution (parameters) ex. X N ( μ, σ 2 ) μ =0? μ = μ 0 ? ex. X N ( μ 1 2 1 ) Y N ( μ 2 2 2 ) μ 1 = μ 2 ? μ 1 2 ? 1 Null( H 0 ): default state, we tend to believe it unless shown otherwise ex: the accused is innocent Alternative( H 1 ): research hypothesis, we do not believe it unless there is an evidence in its favor ex: the accused is guilty Decisions: Reject H 0 : sufficient evidence against H 0 ex. guilty Do not reject H 0 : not much evidence in favor of H 1 ex. not guilty 2 Errors: H 0 true H 1 true Reject H 0 Type I error correct decision Do not reject H 0 correct decision Type II error Type I error = an innocent man goes to jail Type II error = a guilty man is set free Test of a statistical hypothesis: a rule which leads to a decision to accept or reject H 0 Critical region C : subset of A which leads to the rejection of H 0 (Rejection region) 3 Power function: yields the probability of reject- ing H 0 Power: the value of the power fuction at a specific parameter point Significance level α : maximum value of the power function under H 0 , maximum probability of the Type I error (size of C , or size of the
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