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STAB22H3 (130)
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STAB22-C21.docx

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Department
Statistics
Course Code
STAB22H3
Professor
Ken Butler

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CHAPTER 21 - MORE ABOUT TESTS (HYPOTHESIS TESTS) => one-tailed, lower-tailed hypothesis - INDEPENDENCE ASSUMPTION - RANDOMIZATION CONDITION - 10% CONDITION - SUCCESS/FAILURE CONDITION - link P-value to decision to H0, and state conclusion in context - if H0 was true, wouldn't see prop this low, so reject H0 - strong evidence of decline in helmet use - propose course of a'xn if possible - ex. Florida legislators should consider change in law - P-value = probab. that statistic observed is as far, or even farther from hypo val, given that H0 is true - P(observed statistic | H0 is true) - ex. P(we observe 50.7% or less | p = 0.60) - P-Value NOT equal to - P(H0 is true | observed statistic) - when P-value small, H0 is rejected, but doesn't prove it is false - if P-value v.large, just means that what is observed was v.consistent w/ H0 - alpha-threshold - P-value has to fall b4 deciding H0 - setting alpha level of the test (aka significance level of the test) - common alpha levels - 0.05, 0.01, 0.001 - P-values below are said to be signif. - meant to indicate relative strength against H0 Null hypothesis Null hypothesis (H 0 is true (H0) is false Type I error => reject H0 when it is true Reject null Correct outcome hypothesis False positive True positive Falsely convicting an innocent person Type II error => failing to reject H0 when its false Fail to Correct outcome reject null True negative hypothesis False negative Failing to convict guilty person - start by assuming H0 is true - if error in that case, then thats type I - other error can only occur if H0 false, and we fail to reject it (type II) - alpha level - alpha = P(Type I error) - beta = P(Type II error) - power: 1 - beta = P(correctly rejecting H0 when it is false) - can decr. chances of making one error by incr'ing chances of making another - to lower BOTH chances, INCREASE SAMPLE size (ie. collect more data) - alpha, beta are used to determine sample size needed ===================================== WHERE ARE WE GOING? - the reader can decide on their own whether the results of the study are statistically signif by examining the study's - hypo.'s (HA, H0) - concluions from hypo test, how it relates to context - pt of this chap: in-depth exmainaiton of hypo tests main text, p554
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