Pharmaceutical company. A pharmaceutical company is considering investing in a “new and improved” vitamin D supplement for children. Vitamin D, whether ingested as a dietary supplement or produced naturally when sunlight falls upon the skin, is essential for strong, healthy bones.

The bone disease rickets was largely eliminated in England during the 1950s, but now there is concern that a generation of children more likely to watch TV or play computer games than spend time outdoors is at increased risk. A recent study of 2700 children randomly selected from all parts of England found 20% of them deficient in vitamin D.

a) Find a 98% confidence interval for the proportion of children in England who are deficient in vitamin D.

b) Explain carefully what your interval means.

c) Explain what “98% confidence” means.

d) Does the study show that computer games are a likely cause of rickets? Explain.