Find the margin of error and 95% interval for the survey result described. According to a poll of 1283 people, about one-third (34% ) of Americans keep a dog for protection. Marginoferror=square % (Round to the nearest whole number as needed.) Confidence interval is from square % to square %

To find the margin of error and the 95% confidence interval for the survey result, we can use the formula for the margin of error and the confidence interval for a population proportion.<br /><br />Given information:<br />- Sample size (n) = 1283<br />- Sample proportion (p) = 34% = 0.34<br /><br />Step 1: Calculate the margin of error.<br />Margin of error = z * √(p * (1 - p) / n)<br />For a 95% confidence level, the z-score is approximately 1.96.<br />Margin of error = 1.96 * √(0.34 * (1 - 0.34) / 1283)<br />Margin of error = 1.96 * √(0.34 * 0.66 / 1283)<br />Margin of error = 1.96 * √(0.2244 / 1283)<br />Margin of error = 1.96 * 0.0157<br />Margin of error = 0.0308 or 3.08%<br /><br />Step 2: Calculate the 95% confidence interval.<br />Lower limit = p - margin of error = 0.34 - 0.0308 = 0.3092 or 30.92%<br />Upper limit = p + margin of error = 0.34 + 0.0308 = 0.3708 or 37.08%<br /><br />Therefore, the margin of error is 3%, and the 95% confidence interval is from 31% to 37%.