Out of 500 people sampled, 200 preferred Candidate A. Based on this, estimate what proportion of the entire voting population (p) prefers Candidate A.

Question

Use a 99% confidence level, and give your answers as decimals, to three places.

 < p < 

Answer 1

Hello, thank you for taking the time to post your question!

When you’re doing a confidence interval for a population proportion you want to use the general formula

CI = p-hat +/- critical value * sqrt(p-hat(1 – p-hat)/n))

So for this set of data we know that

p-hat = 200/500 = 0.40

n = 500

and the critical value for a 99% confidence level is 2.576

putting that all together means

CI = 0.40 +/- 2.576 * sqrt(0.4(1-0.4)/500)

CI = 0.40 +/- 0.0564

CI: 0.344 to 0.456

Hopefully that gets you moving in the right direction! Feel free to reach out for a lesson if you have any questions beyond that! :)