In 16% of all homes with a stay-at-home parent, the father is the stay-at-home parent (Pew Research, June 5, 2014). An independent research firm has been charged with conducting a sample survey to obtain more current information.

a. What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of .03 (round up to the next whole number)? Use a 95% confidence level.

b. Repeat part (a) using a 99% confidence level (round up to the next whole number).