A certain forum reported that in a survey of 2006 American adults, 24% said they believed in astrology. (a) Calculate a confidence interval at the 99% confidence level for the proportion of all adult Americans who believe in astrology. (Round your answers to three de Interpret the resulting interval. O we are 99% confident that this interval contains the true population mean. O we are 99% confident that this interval does not contain the true population mean. O we are 99% confident that the true population mean lies above this interval. O we are 99% confident that the true population mean lies below this interval. (b) What sample size would be required for the width of a 99% CI to be at most 0.05 irrespective of the value of p? (Round your answer up to the nearest integer.