Question

In the upcoming election for governor, the most recent poll, based on 900 respondents, predicts that the incumbent will be reelected with 55 percent of the votes. What is σρˆ?

.00825
.0166
.0247
.0003

Answer 1

.0166

Explanation:

Central Limit Theorem for proportions:

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean
`\mu = p` and standard deviation
`\sigma_(p) = \sqrt{(p(1-p))/(n)}`

In this question:

`n = 900, p = 0.55`

What is σρˆ?

The standard deviation of the sample proportion, which is:

`\sigma_(p) = \sqrt{(0.55*0.45)/(900)} = 0.0166`