# LCT13 - Introduction to Business Statistics Lecture 13...

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1 Introduction to Business Statistics Lecture 13 Calculations in Hypothesis Testing Test Statistics and Rejection Regions: Choose rejection regions so that α is controlled at a prescribed level Choose test statistics so that for fixed , β is smallest possible Large sample tests for µ with fixed : H 0 := 0 One-Sided Alternatives: H a : > 0 and H a : < 0 Two-Sided Alternative: H a : 0

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2 Test Statistic: z xx n x = = µ σ 00 / Rejection Regions: One-Tailed H a : > 0 H a : < 0 } | { α z z z > } | { z z z < Two-Tailed: Note :5 8 . 2 z 33 . 2 z 96 . 1 645 . 1 z 0.005 0.01 025 . 0 0.05 = = = = z H a : 0 } or | { 2 / 2 / z z z z z < >
3 Solution to Example 3 ( Pollution Control ) 500 : 0 = µ H versus 500 : < a H The rejection region with 01 . 0 = α is } 33 . 2 | { < z z The test statistic 33 . 2 01 . 8 50 / 34 . 125 500 358 / 0 < = = = n x z σ . Because the sample value of the test statistics is in the rejection region, we reject the null hypothesis. That is, the sample data presents significant evidence that the pollution reduction measure adopted by the paper firm is effective.

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4 Large Sample Test for H p p 0 := 0 with Fixed α : One-Sided Alternatives: H p p a : > 0 and H p p a : < 0 Two-Sided Alternative: H p p a : 0 Test Statistic: z p p p p pq n p = =
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## This note was uploaded on 11/23/2010 for the course BBA ISOM111 taught by Professor Hu during the Fall '08 term at HKUST.

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LCT13 - Introduction to Business Statistics Lecture 13...

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