Question

A simple random sample of 1600 persons is taken to estimate the percentage of Democrats among 25000 eligible voters in a certain town. It turns out that 872 people in the sample are Democrats.

We can be 95 percent confident that between ...… percent and ........ percent of the voters are Democrats.

Answer 1

Sample proportion = 872 / 1600 = 0.545

95% confidence interval for p is

- Z * sqrt( ( 1 - ) / n) < p < + Z * sqrt( ( 1 - ) / n)

0.545 - 1.96 * sqrt( 0.545 * 0.455 / 1600) < p < 0.545 + 1.96 * sqrt( 0.545 * 0.455 / 1600)

0.521 < p < 0.569

We can be 95% confident that between 52.1% and 56.9% of the voters are Democrats.