In a recent poll, 470 people were asked if they liked dogs, and 57% said they did. Find the margin of error of this poll, at the 99% confidence level.

Answer 1

To find the margin of error, we first need to find the standard error of the proportion.

The formula for the standard error of the proportion is:

SE = sqrt((p * (1-p)) / n)

where p is the proportion of people who said they liked dogs, and n is the sample size.

First, we need to convert the percentage into a proportion.

p = 57% / 100% = 0.57

Next, we can substitute the values into the formula:

SE = sqrt((0.57 * (1-0.57)) / 470)

Calculating this:

SE = sqrt((0.57 * 0.43) / 470)
= sqrt(0.2451 / 470)
= sqrt(0.00052)
= 0.0228

Finally, to calculate the margin of error, we need to multiply the standard error by the critical value.

At the 99% confidence level, the critical value is 2.576.

Margin of Error = 2.576 * 0.0228
= 0.0589

Therefore, the margin of error of this poll at the 99% confidence level is approximately 0.0589.