According to a Gallup poll of 1012 people, about one-third of (32%) of Americans keep a dog for protection. Find the:

Margin of Error Incorrect% (round to two decimal places)

The 95% Confidence Interval  Incorrect% to Incorrect% (round to two decimal places)

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.

According to a Gallup poll of 1012 people, about one-third of (32%) of Americans keep a dog for protection. Find the: Margin of Error Incorrect% (round to two decimal places) The 95% Confidence Interval Incorrect% to Incorrect% (round to two decimal places)

Learn how to calculate the margin of error and 95% confidence interval based on a Gallup poll, where 32% of Americans keep a dog for protection. Understand the key statistical concepts and formulas, including proportions and Z-scores. Suitable for high school statistics students.

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