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?

To determine the correct statement about the confidence interval, we need to understand what the margin of error and confidence interval represent.

### 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:
The confidence interval is calculated by adding and subtracting the margin of error from the sample proportion.

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

### Interpretation:
The confidence interval suggests that we are 95% confident that the true proportion of the population that would vote for the Center Party lies between 8.7% and 10.3%.

### Correct Statement:
The correct statement is:
- **"We are 95% confident that between 8.7% and 10.3% of the population would vote for the Center Party if there were elections today."**

Would you like more details or have any other questions?

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Here are some related questions you might find useful:
1. What does a confidence level of 95% mean in statistics?
2. How is the margin of error calculated in a poll?
3. What factors affect the width of a confidence interval?
4. How does sample size impact the margin of error?
5. What is the difference between a confidence interval and a prediction interval?
6. How do we interpret confidence intervals in hypothesis testing?
7. What would happen to the confidence interval if the confidence level was increased to 99%?
8. How do we report confidence intervals in research papers?

**Tip:** When interpreting confidence intervals, remember that they provide a range of values within which the true population parameter is likely to lie, given a certain level of confidence.

Explore how confidence intervals and margin of error are used in opinion polls. Learn about the calculation and interpretation of these statistical measures with a practical example. Suitable for advanced high school students and anyone interested in statistics.

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