Question

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

Answer 1

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