Class 5 Louie F1F6 2015 9.22 - STATISTICAL ANALYSIS 1 Week 5 AGENDA LEARNING OBJECTIVES Review of hypothesis testing One way analysis of variance(ANOVA

Class 5 Louie F1F6 2015 9.22 - STATISTICAL ANALYSIS 1 Week...

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STATISTICAL ANALYSIS Week 5 1 9 / 2 6 / 1 5
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AGENDA & LEARNING OBJECTIVES Review of hypothesis testing One way analysis of variance (ANOVA) 2 test of goodness of fit 2 test for independence 2 9 / 2 6 / 1 5
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CHAPTERS WE COVER 10.1, 10.2 11.1, 11.2, 11.3, 11.4 12.2 13.1,13.2,13.3 9 / 2 6 / 1 5 3
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HYPOTHESIS TESTING: POPULATION VARIANCE o For the hypothesis about µ , we used the z and the t distribution. o For 2 , we use 2 distribution 9 / 2 6 / 1 5 4
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HYPOTHESIS TESTING: POPULATION VARIANCE o For the hypothesis about µ , we used the z and the t distribution. o For 2 , we need to know the distribution of s 2 . o When x is normally distributed: [(n-1) s 2 / 2 ] has a 2 distribution with n-1 degrees of freedom. o 2 distribution is not symmetrical and changes the shape with df.
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HYPOTHESIS TESTING: POPULATION VARIANCE: 2 DISTRIBUTION Table A.17; page 875
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EXAMPLE 4 A sample of size 20 drawn from a normal population has s 2 = 6.8. Test the hypothesis that the sample comes from a population with a variance greater than 4.75; = 0.05
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EXAMPLE 4 1. Select H 0 and H a 2. Select 3. Test statistic ? 4. Critical value(s)? 5. Analysis 6. Decision? H 0 : σ 0 2 4.75 H a : σ 0 2 > 4.75 = 0.05 Testing 2 use 2 2 0.05,19 = 30.144 2 = (n – 1) s 2 0 2 = (19 * 6.8/ 4.75) = 27.2 Do not reject H 0 .05 30.144
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1. Has a normal distribution if each sampled population has a normal distribution or sample sizes n 1 and n 2 are large 2. Has a mean of 3. Has standard deviation 9 / 2 6 / 1 5 11 ( x 1 x 2 ) 1 2 ( x 1 x 2 ) 1 2 n 1 2 2 n 2
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HYPOTHESIS TESTING: TWO POPULATION MEANS Two sided OR One sided OR One sided OR We can also test H 0 : µ 1 - µ 2 = D 0 and H 0 : µ 1 - µ 2 ≠ D 0 9 / 2 6 / 1 5 12 2 1 A 2 1 0 µ µ : H µ µ : H 2 1 A 2 1 0 µ µ : H µ µ : H 2 1 A 2 1 0 µ µ : H µ µ : H 0 µ µ : H 0 µ µ : H 2 1 A 2 1 0 0 µ µ : H 0 µ µ : H 2 1 A 2 1 0 0 µ µ : H 0 µ µ : H 2 1 A 2 1 0
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HYPOTHESIS TESTING: TWO POPULATION MEANS: Z TEST When to use?
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