Elected officials in a California city are preparing the annual budget for their community. They would like to estimate how much their constituents living in this city are typically paying each year in real estate taxes. Given that there are over 100,000 homeowners in this city, the officials have decided to sample a representative subset of taxpayers and study their tax payments. Suppose that the officials in this city want to estimate the proportion of taxpayers whose annual real estate tax payments exceed $2000. a. What sample size is required to generate a 99% confidence interval for this proportion with a half-length of 0.10? Assume for now that the relevant population proportion p equals 0.50. b. Assume now that officials discover another source that suggests that approximately 30% of all property owners in this community pay more than $2000 annually in real estate taxes. What sample size is now required to generate the 99% confidence interval requested in part a