Question

Mr. Scoville ran for school board last year and got 18% of the vote. He is running again this year. How many people would need to be surveyed in order to estimate Mr. Scoville’s support to within 4 percentage points with 95% confidence?

Answer 1

To estimate Mr. Scoville's support within 4 percentage points with 95% confidence, at least 621 people would need to be surveyed.

Step-by-step explanation:

To estimate Mr. Scoville's support within 4 percentage points with 95% confidence, we can use the formula for sample size:

n = (
`Z^2` * p * (1-p))/(
`E^2`)

Where:

n is the sample size

Z is the z-score corresponding to the desired confidence level (in this case, 1.96 for 95% confidence)

p is the estimated proportion (18% or 0.18)

E is the desired margin of error (4 percentage points or 0.04)

Plugging in these values, we get:

n = (
`1.96^2` * 0.18 * (1-0.18))/(
`0.04^2`)

n ≈ 620.010

Therefore, at least 621 people would need to be surveyed in order to estimate Mr. Scoville's support to within 4 percentage points with 95% confidence.