show work pleasee
A national polling agency conducted a poll in which an SRS of 3000 Americans that are registered to vote were contacted regarding whether additional taxes should be imposed on gasoline to encourage individuals to purchase more fuel-efficient automobiles. The agency obtained answers from 1200 Americans (out of 3000 who were contacted), and found that 580 would vote for the proposed taxes. Let p represent the proportion of registered voters that would vote for the proposed taxes. Determine a 99% confidence interval for p. How large a sample n would you need to estimate p with margin of error 0.02 with 95% confidence? Use the guess p = 0.5 as the value for p.