Continuing Problem 32, 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 is close to 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?
c. Why is there a difference between your answers to parts a and b?
d. If a random sample of the size from part a is selected and a 99% confidence for the proportion is calculated from this sample, will the half-length of the confidence interval be equal to 0.10? Explain why or why not.