An educator wants to construct a 98%

confidence interval for the proportion of elementary schoolchildren in Colorado who are proficient in reading.

a. The results of a recent statewide test suggested that the proportion is 0.70. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.05?

b. Estimate the sample size needed if no estimate of p is available.

c. If the educator wanted to estimate the proportion in the entire United States rather than in Colorado, would the necessary sample size be larger, smaller, or about the same?
Explain.