Question: Continuing Problem, 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.
Problem: 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 $100? Assume that the best estimate of the population standard deviation is $535.
b. If a random sample of the size from part a is selected and a 95% confidence interval for the mean is calculated from this sample, will the half length of the confidence interval be equal to $100? Explain why or why not.
c. Now suppose that the officials want to construct a 95% confidence interval with a half-length of $75. 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.