Question

In the 1980’s it was generally believed that congenital abnormalities affected 6% of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A 2014 study examined 384 children and found that 28 of them showed signs of an abnormality.

Find and interpret a 95% confidence interval for the proportion of all children with congenital abnormalities in 2014. Find the error bound of the confidence interval. Does this provide evidence that the true proportion of children with congenital abnormalities has changed from the 1980’s to 2014? Justify.

Answer 1

We need to construct the 95% confidence interval for the population proportion. We have been provided with the following information about the number of favorable cases:

Favorable Cases X =	28
Sample Size N =	384

The sample proportion is computed as follows, based on the sample size N = 384 and the number of favorable cases X = 28

The critical value for α=0.05 is z_c = 1.96. The corresponding confidence interval is computed as shown below:

Since, the interval contains 0.06 or 6% hence,  the true proportion of children with congenital abnormalities has not changed from the 1980’s to 2014