Paracetamol (acetaminophen) is the most commonly used analgesic in young children. Some evidence suggests that ingestion of paracetamol in early life may cause asthma in some children. In the study, 495 children with a family history of allergic disease have been exposed to paracetamol in the first two years of life. It was found that 148 of these children have developed asthma between the age of 6 and 7.
(a) Give a 95% confidence interval for the proportion p of children with asthma, in the general population of children who were exposed to parac-etamol in early life and have a family history of allergic disease.
(b) It is estimated that among the children with a family history of allergic disease, 25% have asthma. Is there enough evidence that the proportion p is higher than 25%? Use a test of hypothesis at level (alpha) = 0.01.