The following questions all focus on definitions and concepts. You can easily answer each of these questions without a calculator, since only basic arithmetic is involved. Read each question carefully and focus on what is being asked.
(a) Suppose Alejandro studies a random sample of data on a categorical variable and calculates a 95% confidence interval for the population proportion to be (0.546, 0.674). Determine what the sample proportion must have been, and explain why.
(b) Suppose Brad and Carly plan to collect separate random samples, with Brad using a sample size of 500 and Carly using a sample size of 1500. If Brad plans to construct a 99% confidence interval for the population proportion and Carly plans to construct a 90% confidence interval, who is more likely to obtain an interval that succeeds in capturing the population proportion? Explain.