• a. Suppose a student studies a random sample of data on a categorical variable and calculates a 95% confidence interval for the population proportion to be (.546,.674). Determine what the sample proportion must have been, and explain why.
• b. Suppose two students plan to collect separate random samples, with the first student using a sample size of 500 and the second student using a sample size of 1500. If the first student plans to construct a 99% confidence interval for the population proportion and the second student plans to construct a 90% confidence interval, who is more likely to obtain an interval that succeeds in capturing the population proportion? Explain.
• c. Suppose three students conduct a group project to estimate the proportion of students at their university who are from a different state. They take a random sample of students and find that 20% of their sample of students are from a different state. They then determine the following confidence intervals for the population proportion who are from a different state. One of these is a 90% confidence interval, one is a 99% confidence interval, and one is incorrect. Identify which is which. (In other words, write "90%" below the appropriate interval, "99%" below another, and "incorrect" below the other.)
  • (.116, .284) (176,.344) (.146,.254)