Question

In the 1980s it was generally believed that congenital abnormalities affect 95% 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 recent student examined 384 randomly selected children and found that 46 of them showed signs of an abnormality. Is this strong evidence that the risk has increased?

a) Construct a 90% confidence interval and interpret your result

b) Use your confidence interval from part a) to evaluate the commonly held belief stated in the first sentence of the problem

Answer 1

(A) sample proportion

sample size n = 384

z score for 90% confidence interval is 1.645 (using z distribution table)

Converting to %, 0.0925*100 = 9.25% and 0.1471*100 = 14.71%

(9.25%,14.71%) {rounded to 2 decimals}

(B) it is clear that the confidence interval does not include 5% null value. Thus, we can say that the risk has increased and abonormality affect more than 5% of nation's children