Thank you 8.11 Sherwin and Layfield [1976] present data about protein leakage in

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Thank you

8.11 Sherwin and Layfield [1976] present data about protein leakage in the lungs of male mice exposed to 0.5 part per million of nitrogen dioxide (NO2). Serum fluorescence data were obtained by sacrificing animals at various intervals. Use the two-sided Wilcoxon test, 0.05 significance level, to look for differences between controls and exposed mice. (a) At 10 days: Controls 143 169 95 111 132 150 141 Exposed 152839186 150 10878 PROBLEMS 285 (b) At 14 days: Controls 76 409 72 163 78 Exposed 119 10425 147 200 173

Explanation / Answer

a)

null and alternative hypothesis are ,

Ho : - There is no difference between control and exposed mice.

Ha : There is difference between control and exposed mice.

Now ,

W- = 1 + 5 = 6

W+ =  2 + 3 + 4 + 6 + 7 = 22

n = 7*8/2 = 28 = max(W-,W+) = 22

If the number of pairs is such that n(n+1)/ 2 is large enough (>20), a normal approximation can be used
mu = n(n+1)/4 =7*8/4 = 14
sigma2 = n(n+1)(2n+1)/24 = 7*8*15 / 24 = 35

z = (22 - 14) / sqrt(35)

z = 1.352

Pvalue = P(Z <= 1.352) = 0.912

alpha = 0.05

Pvalue > alpha therefore we do not reject the null hypothesis.

There is not enough evidence that to say there is difference between control and exposed mice.

Similarly solve part-b

Control Exposed diff Sign Rank 143 152 -9 Negative 1 169 83 86 Positive 2 95 91 4 Positive 3 111 86 25 Positive 4 132 150 -18 Negative 5 150 108 42 Positive 6 141 78 63 Positive 7

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