Question

To verify the hypothesis that blood lead levels tend to be higher for children whose parents work in a factory that uses lead in the manufacturing process, researchers examined lead levels in the blood of 33 children whose parents worked in a battery manufacturing factory (Morton, D., Saah, A., Silberg, S., Owens, W., Roberts, M., Saah, M., Lead Absorption in Children of Employees in a Lead-Related Industry,” American Journal of Epidemiology, 115, 549-555, 1982). Each of these children was then matched by another child who was of similar age, lived in a similar neighborhood, had a similar exposure to traffic, but whose parent did not work with lead. The blood levels of the 33 cases (sample 1) as well as those of the 33 controls (sample 2) were then used to test the hypothesis that the average blood levels of these groups are the same. If the resulting sample means and sample standard deviations were ¯ x1 = .015,s1 = .004 and ¯ x2 = .005,s1 = .006, find the result p-value. Assume a common variance.

Answer 1

Given that x1 = .015,s1 = .004 and ¯ x2 = .005,s1 = .006, n1 = n2 = 33

test statistic t =

degree of freedom = n1 +n2 -2 = 33 + 33 -2 = 66 - 2 = 64

using t distribution table with t value (7.97) and df(64) for right tailed hypothesis, we get

p value = 0.0000

p value is less than 0.05 significance level, rejecting the null hypothesis

We can conclude that blood lead levels tend to be higher for children whose parents work in a factory that uses lead in the manufacturing process, researchers examined lead levels in the blood of 33 children whose parents worked in a battery manufacturing factory