We can calculate both the margin of error and the 95% confidence interval based on the given data from the Gallup poll.

1. Margin of Error (MoE): The formula for margin of error for proportions is: $MoE = Z \times \sqrt{\frac{p(1 - p)}{n}}$ where:

   • $Z$ is the Z-value corresponding to the desired confidence level (for 95% confidence, $Z = 1.96$),
   • $p$ is the proportion (32% or 0.32),
   • $n$ is the sample size (1012).

2. 95% Confidence Interval (CI): The 95% confidence interval is calculated as: $CI = p \pm MoE$ Let's calculate the margin of error and the confidence interval now.

Step 1: Compute the margin of error

We'll substitute the values into the formula.### Results:

1. Margin of Error (MoE): 2.87% (rounded to two decimal places).
2. 95% Confidence Interval (CI): 29.13% to 34.87% (rounded to two decimal places).

Would you like more details or have any questions?

Here are 5 related questions you might find useful:

1. How does increasing the sample size affect the margin of error?
2. What is the Z-value for a 99% confidence level, and how would that change the results?
3. How would the results change if 50% of people owned a dog for protection?
4. What is the formula for the margin of error for means instead of proportions?
5. Can you calculate a 90% confidence interval using the same data?

Tip: Reducing the margin of error can be achieved by increasing the sample size or choosing a lower confidence level.