A certain forum reported that in a survey of 2004 American adults, 22% said they believed in astrology. (a) Calculate a confidence interval at the 99% confidence level for the proportion of all adult...

Extracted text: A certain forum reported that in a survey of 2004 American adults, 22% 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 decimal places.) Interpret the resulting interval. O we are 99% confident that the true population mean lies below this interval. O we are 99% confident that this interval does not contain the true population mean. We are 99% confident that the true population mean lies above this interval. O we are 99% confident that this interval contains the true population mean. (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.) You may need to use the appropriate table in the Appendix of Tables to answer this question.