Lecture3_Part6 - F Distribution SUNY at Albany Department...

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SUNY at Albany - Department of Economics F Distribution Eco 320 • Economic Statistics
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SUNY at Albany - Department of Economics Eco 320 • Economic Statistics F-Distribution 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 F (1, 1) F (2, 2)
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SUNY at Albany - Department of Economics Eco 320 • Economic Statistics F-Distribution 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 F (2, 10) F (10, 2)
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SUNY at Albany - Department of Economics Eco 320 • Economic Statistics F-Distribution 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 F (2, 2) F (10, 2) F (50, 50)
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1. F Distribution A. Let ? 1 , ? 2 , … , ? ? be a random sample of size m from a normal distribution X~N(𝜇 ? , 𝜎 ? 2 ) , and let ? 1 , ? 2 , … , ? ? be a random sample of size n from a normal distribution Y~N(𝜇 ? , 𝜎 ? 2 ) . Assume that these two samples are independent. We want to find out whether 𝜎 ? 2 = 𝜎 ? 2 . B. Since we cannot directly observe the two population variances, we use their sample estimator 𝑆 ? 2 = (? 𝑖 −? ) 2 ?−1 and 𝑆 ? 2 = (? 𝑖 −? ) 2 ?−1 C. Statistical theory shows that if 𝜎 ?
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