Suppose that 1 month before the election a random sample of 500 registered voters are surveyed. From this sample 270 indicate that they plan to vote for Smith. Based on this survey data, find the 95% confidence interval estimate of Smith’s current support.

Answer:[ 0.4964, 0.5836 ]Step-by-step explanation:Data provided in the question:Total sample size = 500person voting for smith = 270thus, P( person voting for smith ), p = [tex]\frac{270}{500}[/tex] = 0.54Confidence level = 95%now,standard error, SE = [tex]\sqrt{\frac{p(1-p)}{n}[/tex]orSE = [tex]\sqrt{\frac{0.54(1-0.54)}{500}[/tex]orSE = 0.0223now,Confidence interval = p ± ( z × SE )here, z value for 95% confidence interval is 1.96Confidence interval = [ 0.54 - ( 1.96 × 0.0223 ), 0.54 + ( 1.96 × 0.0223 ) ]= [ 0.54 - 0.0436 , 0.54 + 0.0436 ]= [ 0.4964, 0.5836 ]