Question

A study was conducted to determine the long-term health eects of workplace

exposure to the process of manufacturing the herbicide (2,4,5 trichlorophenoxy)

acetic acid. The outcome of interest was fetal deaths. Suppose the investigators

expect, given general population pregnancy statistics at the tiem of the survey

that 1:5% of pregnancies will result in a fetal death. They found that among 586

pregnancies where an exposed worker was the father, 11 resulted in a fetal death. Is

this enough evidence to claim that exposure to the herbicide has an adverse eect

on survival of children born to men exposed to the herbicide?

Answer 1

Let be the true proportion of pregnancies, when the father is exposed to herbicide, that will result in fetal death. We can say that exposure to the herbicide has an adverse effect on on survival of children born to men exposed to the herbicide if the propotion of fatalities is more than 1.5% that occurs in general population, that is we want to test if

that is we want to test the following hypotheses

We have the following information from a sample of 586 pregnancies

The standard error of the proportion is

Since the value of n*p = 11, and is greater than 5 we use normal distribution for testing the hypotheses

The test statistics is

This is a one tailed test (The alternative hypothesis is >0.015). The critical value of z for significance level alpha =0.05 is given by

Using standard normal tables we get

the sample test statistics of 0.80 is less than the critical value 1.64. That means we do not reject the null hypothesis

We conclude that there is no sufficient evidence to support the claim that exposure to the herbicide has an adverse effect on on survival of children born to men exposed to the herbicide