Question: In the 1980s it was generally believed that congenital abnormalities affect 5% of the nation's children. Some people believe that the increase in the number of chemicals in the environment has lead to an increase in the incidence of abnormalities. A recent study examined 384 children and found that 46 of them showed signs of abnormality. Is this strong evidence that the risk has increased? (We consider P-value of around 5% to represent strong evidence.)

a) Write appropriate hypotheses.
b) Check the necessary assumptions.
c) Perform the mechanics of the test. What is the P-value? Draw a sketch of the distribution of the proportions and your test data. This does not need to be large, but must show the relevant data.

d) Explain carefully what the P-value means in this context.
e) What's your conclusion?
f) Do environmental chemicals cause autism?