A sociologist wants to construct a 95% confidence interval for the proportion of children aged 8–12 living in New York who own a cell phone.

a. A survey by the National Consumers League estimated the nationwide proportion to be 0.56. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.02?

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

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

Explain.