In a random sample of 400 registered voters, 120 indicated they plan to vote for candidate

a. determine a 95% confidence interval for the proportion of all the registered voters who will vote for candidate a

Formula applied: p + / - Z*sqrt (p (1-p) / N)

Where

p=probability of those who will vote for candidate a = 120/400 = 0.3

Z = Critical value at 95% confidence interval = 1.96

N = Size of the sample = 400

Substituting;

Interval = 0.3 + / - 1.96 * sqrt (0.3 (1-0.3) / 400) = 0.3+/-0.045

Interval of population who will vote for candidate a at 95% confidence interval

= 0.3+0.045 to 0.3-0.045

=0.345 to 0.255 of the total population