In a recent poll, 580 people were asked if they liked dogs, and 76% said they did. Find the margin of error of this poll, at the 99% confidence level.

Question

Give your answer to three decimals

Answer 1

To find the margin of error at the 99% confidence level, we can use the following formula:

Margin of Error = Z * (sqrt(p * (1-p) / n))

Where:
- Z represents the z-score associated with the desired confidence level (in this case 99% confidence level)
- p represents the proportion of people who like dogs
- n represents the sample size

First, we need to find the z-score associated with the 99% confidence level. The z-score can be obtained using a standard normal distribution table or a calculator. For a 99% confidence level, the z-score is approximately 2.576.

Given that 76% of the 580 people in the poll said they liked dogs, the proportion (p) is 0.76, which can be written as 0.76/1.

The sample size (n) is 580.

Now we can substitute these values into the margin of error formula:

Margin of Error = 2.576 * (sqrt(0.76 * (1-0.76) / 580))

Calculating this expression yields the following result:

Margin of Error ≈ 0.035

Rounded to three decimals, the margin of error is approximately 0.035.