Lecture28 - ECO220Y Lecture 28 Hypothesis Testing(5 Migiwa...

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ECO220Y Lecture 28 CO220 ectu e 28 Hypothesis Testing (5) Migiwa Tanaka Reading 11.3,4 1

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utline Outline Testing population mean when the population variance is known Two Approaches to Hypothesis Testing Rejection Region Method p-value Method ne il vs two il Test One-tail vs. two-tail Test Calculating the probability of a Type II Error 2
ype I Error and Type II Error Type I Error and Type II Error In hypothesis testing, we may make two types of mistakes. H 0 is true (innocent) H 1 is true (guilty) eject H onvict) ype I rror orrect Decision pe I Error: Rejecting true null hypothesis Reject H 0 (Convict) Type I Error Correct Decision Do not reject H 0 (Acquit) Correct Decision Type II Error Type I Error: Rejecting true null hypothesis. In rejection region method, we set α = maximum Probability(Type I Error) from the test. p -value represents this probability. Type II Error: Failing to Reject false null hypothesis. Probability(Type I Error)= β It depends on: true parameter value, hypotheses, sample size, 3 significance level ( α ).

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Recap of Hypothesis Testing Objective: Test hypotheses Population of X H 0 : μ=100 H 1 : μ>100 015 A Sample, n=170 ? What we get: a sample This is used as a evidence .01 .0 nsity 31.53 s 96.62 X for H 1 .005 De n 4 0 0 50 100 150 200 X
ecap of Hypothesis Testing Recap of Hypothesis Testing From theory, we know the Population of X sampling distribution of mean under different assumption. If the CLT can be applied, e distribution is ormal Sampling Distribution of Mean the distribution is normal . Symmetric oncentration around center n=170 Concentration around center. If the sample is drawn from population assumed in H 0 , the n X V X E / ] [ ] [ 2 chance of getting the sample mean close to the value in H 0 is very high. 5

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ecap of Hypothesis Testing n=170, when H 0 is ture Sampling Distribution of Mean Recap of Hypothesis Testing The further the value of X calculated using your sample from the value in H 0 : μ= μ 0 , H 1 : μ>μ 0 H 0 to the direction of H 1 the stronger/weaker the idence for H H 1 Sampling Distribution of Mean evidence for H 1 The closer the value of lculated using ur X 0 n=170, when H 0 is ture calculated using your sample to the value in H 0 , e ronger/weaker e H 0 0 , the stronger/weaker the evidence for H 1 H 1 : μ μ 0 6 H 1 H 1 0
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• Spring '11
• tanaka
• Null hypothesis, Hypothesis testing, Statistical hypothesis testing, H0, Type I and type II errors, Statistical power

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Lecture28 - ECO220Y Lecture 28 Hypothesis Testing(5 Migiwa...

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