In a survey of 1800 US households, 1278 indicated that they owned a pet. 2. Find the margin of error for a $95 \%$ level of confidence. 3. Construct the $95 \%$ confidence interval.

Step 1 ：First, we calculate the sample proportion (p̂), which is the number of households that own a pet divided by the total number of households surveyed. In this case, we have 1278 households that own a pet out of a total of 1800 households surveyed. So, \(p̂ = \frac{1278}{1800} = 0.71\).

Step 2 ：Next, we calculate the standard error of the proportion. The formula for this is \(\sqrt{\frac{p̂ * (1 - p̂)}{n}}\), where n is the total number of households surveyed. Substituting the values we have, we get \(\sqrt{\frac{0.71 * (1 - 0.71)}{1800}} = 0.010695274138089631\).

Step 3 ：We then calculate the margin of error for a 95% level of confidence. The formula for this is \(Z * \sqrt{\frac{p̂ * (1 - p̂)}{n}}\), where Z is the Z-score for a 95% confidence level, which is approximately 1.96. Substituting the values we have, we get \(1.96 * 0.010695274138089631 = 0.020962737310655677\).

Step 4 ：Finally, we round the margin of error to three decimal places to get the final answer. So, the margin of error for a 95% level of confidence is approximately \(\boxed{0.021}\).