In the past, 26% of all homes with a stay-at-home parent had the father as the stay-at-home parent. 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 0.05? Use a 95% confidence level. (b) Repeat part (a) using a 99% confidence level. Step 1 (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 0.05? Use a 95% confidence level. To get the sample size necessary to obtain a particular margin of error, the following formula will be used where za/2 is the z value corresponding to an upper tail area of level of 1-a, p* is the planning value for the point estimate of the population proportion, and E is the desired margin of error. and a confidence 2 n = (za/2)p*(1 - p*) E The desired margin of error is 0.05 for a 95% confidence level. This confidence level will be used to determine the value of Za/2. Common values for z/2 given belowy for various confidence levels are a Confidence Level a Za/2 2 90% 0.10 0.05 1.645 95% 0.05 0.025 1.960 99% 0.01 0.005 2.576 ording to the table for a 95% confidence level, we have Za/2