Out of 500 people sampled, 235 preferred Candidate A. Based on this, estimate what proportion of the entire voting population

Question

Out of 500 people sampled, 235 preferred Candidate A. Based on this, estimate what proportion of the entire voting population (p) prefers Candidate A.

Use a 95% confidence level, and give your answers as decimals, to three places.

 __ < p- < __

Answer 1

Hi Annie,

Formula for this confidence interval is:

CI= p^ +/- z*SE

To use this, we must have at least ten “successes” and ten “failures.” Defining candidate A preference as success, we clearly have both here, so let’s move on.

p^=sample proportion = 235/500 = 0.470

z* = z-critical value = 1.96 –You should memorize this for 95% confidence level—it comes up a lot in statistics.

SE=standard error, which has its own formula

SE=sqrt(p^q^/n) where

p^=probability estimate = 0.470

q^= 1-p^ = 0.530

n= sample size = 500

SE = sqrt((0.470*0.530)/500)

SE=0.022

Now, we can compute our confidence interval:

CI = 0.470 +/- (1.96*0.022)

CI= (0.426, 0.513) or:

0.426 < p < 0.513

I hope this helps.