Answer:
[ 0.4964, 0.5836 ]
Step-by-step explanation:
Data provided in the question:
Total sample size = 500
person voting for smith = 270
thus,
P( person voting for smith ), p = = 0.54
Confidence level = 95%
now,
standard error, SE =
or
SE =
or
SE = 0.0223
now,
Confidence interval = p ± ( z × SE )
here,
z value for 95% confidence interval is 1.96
Confidence 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 ]