Math Question, need help

Question

Out of 500 people sampled, 135 preferred Candidate A. Based on this, estimate what proportion of the voting population ( p ) prefers Candidate A. Use a 90% confidence level, and give your answers as decimals, to three places.

Answer 1

so first we find the mean proportion: p=x/n=135/500=.27

next we find the standard deviation: sd=sqrt(pq/n)=sqrt(.27*.73/500)=.0199

then find the upper and lower bounds at a 90% confidence level (critical value of 1.645):

upper bounds=p+z*sd=.27+1.645*.0199=.3027

lower bounds=p-z*sd=.27-1.645*.0199=.2373

The 90% confidence interval is (.237,.303)