Chapter 10

# Chapter 10 - Chapter 10 HYPOTHESIS TESTING FOR TWO...

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1 Chapter 10 HYPOTHESIS TESTING FOR TWO POPULATION MEANS AND VARIANCES AND SAMPLE SIZES FOR HYPOTHESIS TESTING (NOT IN BOOK)

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2 Testing Equality of 2 Variances
3 Special Property:

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4 A quality control engineer wants to find out whether or not a new machine that fills bottles with liquid has less variability than the machine currently in use. The engineer calibrates each machine to fill bottles with 16 ounces of liquid. After running each machine for 5 hours, she randomly selects filled bottles from each machine and measures their contents. She obtains the following results. Old machine: n=15, sample mean = 16.0053, s=0.07586 New machine: n=16, sample mean =16.0020, s=0.04586 Test to see if the new machine has less variability (smaller variance) at the .01 significance level.
5 Hypotheses: Test Statistic Calculation: Rejection Region: Decision: Conclusion:

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6 Testing on Means for Two Populations Deciding on which test to conduct for two means is not as simple as deciding between a t test and z test. We have different test statistics depending on: - whether the samples are independent (Is the data collected in pairs? Or from independent samples) - whether we know sigma (population standard deviation) for the two populations - when using s, whether we believe the underlying populations have equal variances.
7 Flowchart For Two Population Means Conduct a hypothesis test for equality of two variances to determine this! Note: All of these methods assume the population is normal or that the Central Limit Theorem applies. #1 #2 #3 #4 must use sample variance as an estimate

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8 Independent Populations, Sigma Known Hypotheses: H 0 : μ 1 2 = ∆ 0 or μ 1 = μ 2 H 1 : μ 1 2 0 , μ 1 2 < ∆ 0 , μ 1 2 does not equal 0 OR μ 1 does not equal μ 2 , μ 1 < μ 2 , μ 1 μ 2 Note: We generally use 0 =0 unless a different value is specified. . #1
9 Independent Populations, σ Unknown but Equal Variances (Pooled T-test) Hypotheses: H 0 : μ 1 2 = ∆ 0 or μ 1 = μ 2 H 1 : μ 1 2 0 , μ 1 2 < ∆ 0 , μ 1 2 does not equal 0 OR μ 1 does not equal μ 2 , μ 1 < μ 2 , μ 1 μ 2 Test Statistic: 2 1 0 2 1 1 1 ) ( n n s x x t p + - - = where 2 ) 1 ( ) 1 ( 2 1 2 2 2 2 1 1 2 - + - + - = n n s n s n s p #2

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10 We are given the following information regarding samples from 2 independent populations, each following a
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Chapter 10 - Chapter 10 HYPOTHESIS TESTING FOR TWO...

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