Continuing Problem 32 suppose that the officials in this city
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.

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