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.
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.