# inference2 - Statistical Inference Point Estimation...

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1 - Mike Pore - Oct 2005 Statistical Inference Statistical Inference Point Estimation Interval Estimation Prediction Intervals Confidence Intervals Hypothesis Testing

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2 - Mike Pore - Oct 2005 Hypothesis Testing Hypothesis Testing H O : μ = μ O Null Hypothesis A A Simple Alternative Complex Alternative
3 - Mike Pore - Oct 2005 Hypothesis Testing Hypothesis Testing Decision Alternatives Decision Alternatives O } Fail to Reject H 0

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4 - Mike Pore - Oct 2005 Hypothesis Testing Hypothesis Testing Decision Alternatives Decision Alternatives Correct Decision Type II error Prob = β Type I error Prob = α Correct Decision The ‘State of Nature:’ reality H 0 is true H A is true Fail to Reject Decisions H 0 (using the data) Reject H 0 Type I error: risk of incorrectly rejecting the null hypothesis, H 0 , when it is true. Type II error: risk of incorrectly failing to reject the null hypothesis, H 0 , when it is false.
5 - Mike Pore - Oct 2005 Hypothesis Testing Hypothesis Testing Simple Alternative Simple Alternative H O : μ = μ O Null Hypothesis H A : μ = μ A Alternate Hypothesis Distribution of when H 0 is true Prob of Type I error = α Threshold for deciding between the hypotheses μ 0 Terms α = level of significance (1- α )100% = confidence level x

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6 - Mike Pore - Oct 2005 Hypothesis Testing Hypothesis Testing Simple Alternative Simple Alternative H O : μ = μ O Null Hypothesis H A : μ = μ A Alternate Hypothesis Distribution of when H 0 is true Prob of Type I error = α Threshold for deciding between the hypotheses μ 0 Decision rules A x x x
7 - Mike Pore - Oct 2005 Hypothesis Testing Hypothesis Testing Complex Alternative Complex Alternative H O : μ = μ O Null Hypothesis H A : μ > μ 0 Alternate Hypothesis Distribution of when H 0 is true Prob of Type I error = α Threshold for deciding between the hypotheses μ 0 Decision rules 0 x x x

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8 - Mike Pore - Oct 2005 Hypothesis Hypothesis Testing Testing Simple Alternative Simple Alternative O O Distribution of when H 0 is true Prob of Type I error = α Threshold for deciding between the hypotheses μ 0 x Distribution of when H A is true x μ A Prob of Type II error = β
9 - Mike Pore - Oct 2005 Hypothesis Hypothesis Testing Testing Simple Alternative Simple Alternative O O Distribution of when H 0 is true Prob of Type I error = α Threshold for deciding between the hypotheses μ 0 x Distribution of when H A is true x μ A Prob of Type II error = β

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10 - Mike Pore - Oct 2005 Hypothesis Hypothesis Testing Testing Simple Alternative Simple Alternative O O Distribution of when H 0 is true Prob of Type I error = α Threshold for deciding between the hypotheses μ 0 x Distribution of when H A is true x μ A Prob of Type II error = β
11 - Mike Pore - Oct 2005 H O : μ = 170 level of significance: α = .05 H A : μ = 176 1 7 0 x b Hypothesis Testing Exercise Hypothesis Testing Exercise when when σ σ is known is known

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Mike Pore - Oct 2005 H O : μ = 170 level of significance: α = .05 H A : μ = 176
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## This note was uploaded on 04/26/2010 for the course ECO 329 taught by Professor K during the Spring '08 term at University of Texas at Austin.

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inference2 - Statistical Inference Point Estimation...

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