In an opinion poll, 9.5% stated that they would have voted for the Center Party if there were "elections today". The margin of error for this was 0.8 percentage points at the 95% confidence level. The result and the margin of error together form a confidence interval. Which statement is correct? Is it 10.8% is within the confidence interval, 8.5% is outside the confidence interval, 9.2% is outside the confidence interval, 10.6% is within the confidence interval or 5.6% is within the confidence interval.

Let's first determine the confidence interval based on the given information:

### Given:
- **Sample proportion (p)**: 9.5% or 0.095
- **Margin of error (E)**: 0.8 percentage points or 0.008
- **Confidence level**: 95%

### Confidence Interval:
- **Lower bound**: \( 0.095 - 0.008 = 0.087 \) or 8.7%
- **Upper bound**: \( 0.095 + 0.008 = 0.103 \) or 10.3%

### Evaluating the Statements:
1. **10.8% is within the confidence interval**: **Incorrect**  
   - 10.8% is above 10.3%, so it is **outside** the interval.

2. **8.5% is outside the confidence interval**: **Correct**  
   - 8.5% is below 8.7%, so it is **outside** the interval.

3. **9.2% is outside the confidence interval**: **Incorrect**  
   - 9.2% falls between 8.7% and 10.3%, so it is **inside** the interval.

4. **10.6% is within the confidence interval**: **Incorrect**  
   - 10.6% is above 10.3%, so it is **outside** the interval.

5. **5.6% is within the confidence interval**: **Incorrect**  
   - 5.6% is far below 8.7%, so it is **outside** the interval.

### Conclusion:
The correct statement is: **8.5% is outside the confidence interval.**

Would you like more details or have any other questions?

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Here are some related questions you might find useful:
1. How do you calculate a confidence interval from a given proportion?
2. What does it mean for a value to be within or outside a confidence interval?
3. How does the sample size influence the margin of error?
4. What are some common misconceptions about confidence intervals?
5. How do we interpret confidence intervals in the context of public opinion polls?
6. Can the confidence interval ever include values like 0% or 100%?
7. What would the confidence interval be if the margin of error were smaller?
8. How can we reduce the margin of error in a poll?

**Tip:** Always ensure to verify that any statement about a confidence interval takes into account the calculated range, not just the central value of the estimate.

Explore how confidence intervals are calculated in opinion polls. Analyze a specific example where 9.5% of respondents favored the Center Party with a margin of error of 0.8 percentage points at a 95% confidence level. Learn which percentages are within or outside the confidence interval.

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