35 Lecture 8 - Inference for Variances

# 35 Lecture 8- - Lecture8 Chapter10 1 2 3 4 5 Nullhypothesis,H0 ,HA Rejectionregion Teststatistic pvalue(ifpossible 2 Whatwillchang

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Lecture 8: Inference for Variances For one and two populations Prepare for an easy ride  Chapter 10

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2 The 5 hypothesis test steps 1. Null hypothesis, H 0 2. Alternative hypothesis, H A 3. Rejection region 4. Test statistic 5. p-value (if possible)
3 The steps remain the same… What will change: The parameter we make inferences about:  Single variance Ratio of variances The distributions we use for our critical  values:  χ distribution F-distribution

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Inference for a Single Variance Hypothesis Test Confidence Intervals
5 Example An inventory management model is  being used that is sensitive to the  standard deviation of the daily demand.   Currently the model is calibrated to a  standard deviation of 12 units per day.   You decide to see if this is still valid,  based on the past 22 days.  In this  sample, the standard deviation is 10.2.   Use  α  = 0.05

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6 H O :   σ 2  = 144 H A σ 2    144 We have to perform the test on the  variances , not the standard deviations Remember this! This is a two-tailed test
7 Inference for a Single Variance The appropriate distribution for a single  variance is the  chi-squared  ( χ 2 pronounced “ki”, rhyming with “eye”)

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8 The  χ Distribution The  χ 2  distribution is not symmetrical, so  we need to look up two values in 2-tailed  situations. Like the t-distribution, the  χ 2  is a function of  the number of degrees of freedom The table is quite similar to the t, except  that two values are given for every  α Table: Appendix G, page 746
Demonstrate  χ 2  Distribution CPD.xls

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## This note was uploaded on 09/25/2010 for the course OMIS OMIS 1000 taught by Professor Alexandershoumarov during the Fall '09 term at York University.

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35 Lecture 8- - Lecture8 Chapter10 1 2 3 4 5 Nullhypothesis,H0 ,HA Rejectionregion Teststatistic pvalue(ifpossible 2 Whatwillchang

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