On the ballot, Illinois voters had the option to select "yes" or "No" when asked if the state's minimum wage should be increased from $8.25 to $10 an hour by January 1, 2015. Before the actual voting date, a survey with a sample size of 50 found that 61.75% percent of respondents supported the minimum wage.
1) Calculate the 95% and 90% confidence intervals for the minimum wage vote.
2) After the election, the results of vote turned out that 62% percent voters answered "yes". Do the confidence intervals include the true mean?
3) If the true support rate is 0.6175, what is the sample size should be if we allow 0.05 of margin of error at 95% confidence level?