Question

A simple random sample of 1600 persons is taken to estimate the percentage of Democrats among...

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.

Homework Answers

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 .

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