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, a. What sample size is required to generate a 95% confidence interval for the mean annual real estate tax payment with a half-length of $1007 Assume that the best estimate of the population standard deviation o is $535 b. If a random sample of the size from part als selected and a 95% confidence interval for the mean is calculated from this sample, will the halflength of the confidence interval be equal to $100? Explain why or why not. The half-length of the confidence interval be equal to $100 only if the sample standard deviation of the sample is select $535 c. Now suppose that the officials want to construct a 95% confidence interval with a half-length of 575. What sample size is required to achieve this objective? Again, assume that the best estimate of the population standard deviation is $535. Explain the difference between this result and the result from part a The required sample size is inversely proportional to Select hall-length