CH-10 PPT - Testing hypotheses about proportions Tests of...

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Testing hypotheses about proportions
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Tests of significance § The reasoning of significance tests § Stating hypotheses § The P -value § Statistical significance § Tests for a population proportion § Confidence intervals to test hypotheses
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Reasoning of Significance Tests Example: A coin is toss 500 times. It lands heads 275 times, which is a bit more than we expect. Is the coin fair or not? Is the somewhat higher number of heads due to chance variation? Is it evidence that the coin is not fair? x
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Stating Hypotheses Situation: We observe some effect and we have two explanations for it: 1) the effect is due to chance variation 2) the effect is due to something significant How to decide? Statement 1) = null hypothesis H 0 (the coin is fair) Statement 2) = alternative hypothesis H a (the x
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The null hypothesis is a very specific statement about a parameter of the population(s). It is labeled H 0 and states “status quo”, previous knowledge, “no effect”, “the observed difference is due to chance”. It is the one which we want to reject. The alternative hypothesis is a more general statement about a parameter of the population(s) that is the opposite of the null hypothesis. It is labeled Ha and is the one we try to prove. Coin tossing example: H 0 : p = 1/2 ( p is the probability that the coin lands heads) Ha : p ≠ 1/2 ( p is either larger or smaller)
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Analogy with a criminal trial H 0 : the defendant is innocent If sufficient evidence is presented, the jury will reject this hypothesis and conclude that H a : the defendant is guilty
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One-sided and two-sided tests A two-tail or two-sided test of the population proportion has these null and alternative hypotheses: H 0 : p = p 0 [a specific proportion] Ha : p p 0 A one-tail or one-sided test of a population proportion has these null and alternative hypotheses: H 0 : p = p 0 [a specific proportion] Ha : p < p 0 OR H 0 : p = p 0 [a specific proportion] Ha : p
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The P-value Example-cont’d: A coin is tossed 500 times. It lands heads 275 times. H 0 : p = 1/2 vs. Ha : p ≠ 1/2
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  • Spring '08
  • Bulmash
  • Null hypothesis, Statistical hypothesis testing, Statistical significance, National Institute for Occupational Safety and Health

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