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 Z 2 is the z value corresponding to an upper tail area of and a confidence 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 2 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 Z 2 Common values for 2 2 for various confidence levels are given below n Confidence Level 90 95 99 R 0 10 a 2 0 05 1 645 0 05 0 025 Za 2 0 01 0 005 1 960 2 576 to the table for a 95 confidence level we have Za 2