You conduct a poll for a candidate You ask 1005 people if th

You conduct a poll for a candidate. You ask 1005 people if they support the candiate and 475 claim they support the candidate. What is the 95% Confidence Interval for the True rate at which the candidate has support?

Question 19 options:

(0.4888330, 0.5303032)

(0.4705635, 0.5255517)

(0.4730963, 0.5054839)

(0.4241356, 0.5089673)

(0.4417706, 0.5035031)

(0.3948545, 0.5320071)

Solution

Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=475
Sample Size(n)=1005
Sample proportion = x/n =0.4726368
Confidence Interval = [ 0.4726368 ±Z a/2 ( Sqrt ( 0.4726368*0.5273632) /1005)]
= [ 0.4726368 - 1.96* Sqrt(0.000248) , 0.4726 + 1.96* Sqrt(0.000248) ]
= [ 0.4417706,0.5035031]