010+Correlation

074 df 22 so the hypothesis h0 does not reject but the

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Unformatted text preview: 1 Restaurant 2 1 1005 918 2 2073 1971 3 873 825 4 1074 999 5 1932 1827 6 1338 1281 7 1449 1302 8 759 678 9 1905 1782 10 693 639 11 2106 2049 12 981 933 9 A. Zhensykbaev Correlation Apply two-tailed test with α = 0.05: H0 = {µ1 − µ2 = 0}, Ha = {µ1 − µ2 = 0}, t-statistic is t= x1 − x2 ¯ ¯ s2 p n1 + s2 p , s2 p (n1 − 1)s2 + (n2 − 1)s2 1 2 = = 273630.6, (n1 − 1) + (n2 − 1) n2 t = 0.384. Reject region RR = {|t| > tα/2 = 2.074 (df = 22). So, the hypothesis H0 does not reject. But the sales of restaurant 1 exceed those of restaurant 2 for every one of the 12 days. It means that we can not apply this test: one of the assumptions of an applicability of t-statistic to test H0 is not true. Let us test the independence using Spearman's test with α = 0.05. Day Restaurant 1 Rank ui Restaurant 2 Rank vi di = ui − vi 1 1005 5 918 4 1 2 2073 11 1971 11 0 3 873 3 825 3 0 4 1074 6 999 6 0 5 1932 10 1827 10 0 6 1338 7 1281 7 0 7 1449 8 1302 8 0 8 759 2 678 2 0 9 1905 9 1782 9 0 10 693 1 639 1...
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This note was uploaded on 02/11/2014 for the course MATH 1390 taught by Professor Christopherstocker during the Spring '13 term at Marquette.

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