8.74 Insomnia in France A team of scientific researchers conducted a study on insomnia in France (Journal of Sleep Research, 9(1):35–42, April 2000). They used a representative sample of the French population that included 12,778 individuals. Among them, 73% complained of a nocturnal sleep problem.

a. Show that this sample has the characteristics required for a population proportion estimate.

b. Construct a 99.9% confidence interval for the population proportion who complained of a nocturnal sleep problem. Explain why the interval is so narrow, even though the confidence level is high.