Question

# In the 1980s it was generally believed that congenital abnormalities affect 95% of the nation's children....

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

(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