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 856 people in the sample are Democrats. We can be 95 percent confident that between percent and percent of the voters are Democrats.

Answer 1

Solution :

Given that,

n = 1600

x = 856

Point estimate = sample proportion = = x / n = 856 / 1600 = 0.535

1 - = 0.465

Z_/2 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.535 * 0.465) / 1600)

= 0.024

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.535 - 0.024 < p < 0.535 + 0.024

0.511 < p < 0.559

We can be 95 percent confident that between 51.1% and 55.9% of the voters are Democrats .