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2106
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2049
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981
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Calculate the test statistic rs using shortcut formula:
12 d2 = 2, rs = 1 −
i
i=1 6·2
= 0.993.
12 · (122 − 1) Thus, rs = 0.993 > 0.497 = rsα , and we reject H0 = {ρ = 0}. Two
samples are correlated and one may not use twosamples tstatistic to test
10 A. Zhensykbaev Correlation H0 = {µ1 − µ2 = 0} if samples are normally distributed. We apply another
test. Paired dierence experiment for two population means.
Assumptions:
1. Both populations are approximately normally distributed;
2. Samples are randomly selected;
(we do not require that the samples are independent and the population
variances are equal). Largesample
Paired dierence condence interval.
sd
σd
¯
¯
d ± zα/2 √ ≈ d ± zα/2 √ ,
nd
nd
where ¯¯
d = x1 − x2 ,
¯
sd  sample standard deviation of dierences,
nd  number of dierences (number of pairs). Paired dierence test of hypothesis for µd = µ1 − µ2 .
The null hypothesis is H0 = {(µd = µ1 − µ2 = D0 },
Alternative hypothes...
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 Spring '13
 ChristopherStocker
 Math, Correlation, Normal Distribution, Probability, Null hypothesis, Probability theory, Statistical hypothesis testing, probability density function, A. Zhensykbaev

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