420Hw07 - x y – y = Σ x – x y = 252 a Test H ρ = 0 vs...

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STAT 420 Fall 2008 Homework #7 (due Friday, October 17, by 3:00 p.m.) From the textbook: 5.7 5.21 3. A society of bird watchers has collected data from several towns on stork sighting ( x ) and human births ( y ) to test the widely expressed belief that storks bring babies. Assume that ( X , Y ) have a bivariate normal distribution. The data are given in the table below: Storks, x 18 16 10 20 14 26 22 Babies, y 27 15 13 21 19 39 27 Σ x = 126, Σ y = 161, Σ x 2 = 2,436, Σ y 2 = 4,175, Σ x y = 3,150, Σ ( x x ) 2 = 168, Σ ( y y ) 2 = 472, Σ ( x
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Unformatted text preview: x ) ( y – y ) = Σ ( x – x ) y = 252. a) Test H : ρ = 0 vs. H a : > 0 at the α = 0.01 level of significance. What can you say about the p-value of this test? b) Does it follow from part (a) that storks do bring babies? Explain . c) Test H : = 0.50 vs. H a : > 0.50 at the α = 0.05 level of significance. What can you say about the p-value of this test? d) Construct a 95% confidence interval for . 100 ( 1 – α ) % confidence interval for : & & ± ² ³ ³ ´ µ +-+-1 1 , 1 1 b b a a e e e e , where 3 2 1 1 2 ln---+ = n r r a z α , 3 2 1 1 2 ln-+-+ = n r r b z ....
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This note was uploaded on 05/09/2010 for the course MATH 420 taught by Professor Stepanov during the Spring '10 term at University of Illinois, Urbana Champaign.

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