stat1801_8

Stat1801_8 - Hypothesis Testing ≠ = 118 118 1 μ μ H H Statistical Hypothesis A statement about population Null hypothesis H Alternative

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Unformatted text preview: Hypothesis Testing ≠ = 118 : 118 : 1 μ μ H H Statistical Hypothesis A statement about population Null hypothesis : H Alternative hypothesis : H 1 ≠ = 1 : 1 : 2 1 2 σ σ H H ≠ = 2 1 1 2 1 2 : 2 : p p H p p H ≠ = 2 2 1 2 2 : : y x y x H H σ σ σ σ on. distributi normal a not is Population : on. distributi normal a is Population : 1 H H Hypothesis Testing Test Procedure (based on sample) leads to rejection or non-rejection of the hypothesis Example : mean IQ of HKU students dropped 118 : vs 118 : Test 1 < = μ μ H H " . 113 if Reject " < X H is a reasonable test. Draw a sample 110 = X Reject H Conclude that μ < 118 But we may be wrong ! Two Types of Errors H 1 H H H Accept H Reject H H 0 true Correct decision Type I error ( H false) H 1 true Type II error Correct decision ( 29 true | Reject H H P = α ( 29 true | Accept 1 H H P = β Type I error probability Type II error probability Two Types of Errors Example : life time of light bulbs with σ = 300 hours 1240 : vs 1200 : 1 = = μ μ H H Test " . 1249 if Reject " X H 100 300 , ~ 2 μ N X Draw a sample with size 100. ( 29 true | Reject H H P = α ( 29 1200 | 1249 = = μ α X P - Φ- = 100 300 1200 1249 1 ( 29 0513 . 633 . 1 1 = Φ- = ( 29 true | Accept 1 H H P = β ( 29 1240 | 1249 = ≤ = μ β X P - Φ = 100 300 1240 1249 ( 29 6179 . 3 . = Φ = 6179 . = β Two Types of Errors 1200 1240 H H 1 1249 0513 . = α increased β reduced α X of on distributi Sampling Type II error Jail an innocence. Choice of H and H 1 α β α β α β α β α β α β α β For fix n , we can only control one of the errors. Convention : Control α . Criterion 1 : Type I error as a more serious error. Example : Want to know if a man is guilty. guilty. is He : H guilty. not is He : 1 H Type I error Release a criminal. More serious error Type II error Jail an innocence. guilty. not is He : H guilty. is He : 1 H Type I error Jail an innocence. Type II error Release a criminal. More serious error Choice of H and H 1 Convention : Control α to be small. Criterion 2 : Put what you want to establish in H 1 . P (false rejection of H ) = P (reject H | H true) = α P (false acceptance of H ) = P (accept H | H 1 true) = β May be large Reject H Strong conclusion Accept H Weak conclusion Do not reject Choice of H and H 1 Criterion 2 : Put what you want to prove in H 1 ....
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This note was uploaded on 02/01/2012 for the course STAT 1801 taught by Professor Mrchung during the Fall '10 term at HKU.

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Stat1801_8 - Hypothesis Testing ≠ = 118 118 1 μ μ H H Statistical Hypothesis A statement about population Null hypothesis H Alternative

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