In a recent poll, 580 people were asked if they liked dogs, and $53 \%$ said they did. Find the margin of error of this poll, at the $95 \%$ confidence level. Give your answer to three decimals Question Help: Message instructor

Step 1 ：Define the variables: the z-score for a 95% confidence level is \(z = 1.96\), the proportion of people who said they liked dogs is \(p = 0.53\), and the sample size is \(n = 580\).

Step 2 ：Calculate the margin of error using the formula: \(margin\_of\_error = z \times \sqrt{\frac{p \times (1 - p)}{n}}\).

Step 3 ：Round the result to three decimal places to get the final margin of error.

Step 4 ：The final margin of error of this poll, at the 95% confidence level, is \(\boxed{0.041}\).