010+Correlation

Rejection region is rr rs rs2 rs rs2 rs

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Unformatted text preview: 10 customers. Customer Income Rank Total Rank number ui borrowed vi 1 14800 5 4300 7 2 8900 1 4800 8 3 83600 10 500 2 4 22100 8 3300 5 5 18200 7 5500 9 6 13700 4 3700 6 7 41800 9 0 1 8 9300 2 3200 4 9 12700 3 6100 10 10 16100 6 1800 3 8 A. Zhensykbaev Correlation Solution. The null hypothesis about a correlation coecient is H0 = {ρ = 0}. Alternative hypothesis is Ha = {ρ = 0}. Rejection region is RR = {rs ≥ rsα/2 } ∪ {rs ≤ −rsα/2 } = {|rs | ≥ rsα/2 }. where rsα/2 = 0.648 is dened from the Table XVII (McClave and Benson) for n = 10. Calculate the test statistic rs : 10 10 ui = i=1 10 vi = 55, i=1 10 u2 i i=1 2 vi = 385, = i=1 SSuv = −47.5, SSuu = SSvv = 82.5, rs = Using shortcut formula we have: 10 (ui − vi )2 = 260, rs = 1 − i=1 −47.5 = −0.5758. 82.5 6 · 260 = 1 − 1.5758 = −0.5758. 10 · 99 So, 0.5758<0.648 and we do not reject H0 . Example 3. Compare the mean daily sales of two restaurants located in the same city.Daily sales for each of 12 randomly selected days are Day Restaurant...
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