The pew forum on religion and public life reported that in a survey of 2003 american adults, 25% said they believed in astrology. (a) calculate and interpret a confidence interval at the 99% confidence level for the proportion of all adult americans who believe in astrology. (b) using the point estimate of p obtained from the survey, what sample size is needed to be 99% confident that the error in estimating the true value of p is less than 0.025? (c) what sample size would be required if you wish to be at least 99% confident that the error in estimating p is at most 0.025, irrespective of the value of ˆp?