A survey was taken of 850 people in a neighborhood, and the results were that 230 people were planning on voting for a particular candidate. Determine the margin of error for a 99% confidence interval of population proportion of people in a neighborhood who were planning on voting for this candidate. Round it to the nearest hundredth and interpret its meaning in context.(2 points)

Question

A survey was taken of 850 people in a neighborhood, and the results were that 230 people were planning on voting for a particular candidate. Determine the margin of error for a 99% confidence interval of population proportion of people in a neighborhood who were planning on voting for this candidate. Round it to the nearest hundredth and interpret its meaning in context.(2 points)
The margin of error=
. With 99% confidence, the population proportion of people in a neighborhood who are planning on voting for a particular candidate falls between 
 and 
.

GPT 3.5 · Answer

The margin of error can be calculated using the formula:

Margin of error = 2.576 * sqrt((p*(1-p))/n)

Where p is the sample proportion (230/850) and n is the sample size (850).

Plugging in the values:

Margin of error = 2.576 * sqrt((230/850)*(1-230/850)/850)
= 0.0311

Therefore, the margin of error is approximately 0.03.

With 99% confidence, the population proportion of people in a neighborhood who are planning on voting for a particular candidate falls between 0.199 and 0.281. This means that we are 99% confident that the true population proportion of people planning on voting for the candidate lies within this range.