Question

5. The paper "Measuring the exposure of infants to tobacco smoke," (New England Journal of Medicine, 1984, pp. 1075-1078) compared infants who had been exposed to household smoke with those that hadn't. The data are observations of urinary concentra- tion of cotamine, a major metabolite of nicotine. Adapt the Wilcoxon rank sum statistic, W, to test whether the mean cotanine level in the population of exposed children is more than 25 units higher than that of unexposed children. Use W to form a confidence interval for the difference, Δ, between the means of the two populations Unexposed: 8,11,12,14, 20, 43, 111 Exposed: 35,56,83, 92, 128, 150, 176, 208 You will find eract critical values of W on the web, in standard statistical tertbooks and in statistical software, such as R. You can find an approrimation to the correct p-value by doing appropriate random permutations of the samples in R. Alternatively you can use the normal approrimation to the null distribution of w.

Answer 1

## R output

> Unexposed=c(8,11,12,14,20,43,111)
> Exposed=c(35,56,83,92,128,150,176,208)
>
>
> wilcox.test(x=Unexposed, y = Exposed,
+ alternative = "less",
+ mu = 25, conf.level = 0.95)

Wilcoxon rank sum test

data: Unexposed and Exposed
W = 3, p-value = 0.001088
alternative hypothesis: true location shift is less than 25

## Comment: The estimated p-value is 0.001088 and less than 0.05 level of significance. Hence, we reject the null hypothesis and accept the claim that the mean cotinine level in the population of exposed children is more than 25 units higher than that of unexposed children at 0.05 level of significance.