Lecture16

# Lecture16 - AMS312 Spring 2010 April 19th Chapter 7(Section...

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Unformatted text preview: AMS312 Spring_ 2010 April 19th Chapter 7 (Section 7.5): Two-sample problems: Review: Inference on two population means, paired samples: the paired differences follow a normal distribution Example 1. Do fraternities help or hurt your academic progress at college? To investigate this question, 5 students who joined fraternities in 1998 were randomly selected. It was shown that their GPA before and after they joined the fraternities are as follows. Please test the hypothesis at α =0.05 Student 1 2 3 4 5 Before 3 4 3 3 2 After 2 3 3 2 1 Diff. 1 1 1 1 Solution: : : ≠ = d a d H H μ μ Assumption : the difference follows a normal distribution. 05 . , 5 , 447 . , 8 . = = = = α n S X d d Test statistic : 1 ~-- = n H d d t n S X T 4,0.025 4.02 2.776 T t = = We reject H at α =0.05 and conclude fraternities does hurt… Review: Inference on two population means, independent samples: Pooled variance t-test: Both samples are from normal populations. Furthermore, 2 2 2 1 2 σ σ σ = = (we can test this using the F-test), population variances are unknown but equal. New: F-test: Data: 1 2 1 1 1 , , ( , ) iid n X X N μ σ K : 2 2 1 2 2 , , ~ ( , ) iid n Y Y N μ σ K 1 AMS312 Spring_ 2010 April 19th 2 1 2 2 2 1 2 2 2 2 2 1 2 1 2 2 : 1 : : : 1 a a H H H H σ σ σ σ σ σ σ σ = = ⇔ ≠ ≠ 1 Point estimator: · ¶ ¶ 2 2 2 1 1 1 2 2 2 2 2 2 ( ) S S σ σ σ σ = = 2 P.Q: Definition : F-Distribution Let 1 2 1 ~ k W χ , 2 2 2 ~ k W χ , and 1 W , 2 W are independent. Then 1 2 1 1 , 2 2 / ~ / k k W k F F W k = Q 1 2 2 1 1 1 2 1 ( 1) ~ n n S χ σ-- 2 2 2 2 2 1 2 2 (...
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Lecture16 - AMS312 Spring 2010 April 19th Chapter 7(Section...

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