Question

What percent of eligible Americans vote? In 2008, a random sample of 500 American adults was

taken and we found that 68% of them voted. How many of the 500 adults in the sample voted?

Now construct a 95% confidence interval estimate of the population percent of Americans that

vote and write a sentence to explain the confidence interval.

Answer 1

a) Number of 500 adults who voted is computed here as:

= np = 500*0.68 = 340

Therefore 340 out of the 500 voters voted.

b) From standard normal tables, we have:

P( -1.96 < Z < 1.96) = 0.95

Therefore the population proportion 95% confidence interval here is computed as:

Therefore the 95% confidence interval for the percentage of American population that votes is given as: (63.91%, 72.09%)

In words, the interpretation of this is that there is a 95% probability that the true percentage of Americans who vote lies in the above interval.