Compare a confidence interval of 99% to 95%. Select all of the below statements that are true.

We have a smaller range of numbers in the 99% confidence interval.

From 95% to 99% confidence interval, we increase the confidence level.

The 99% confidence interval is larger and contains less numbers.

From 95% to 99% confidence interval, we lose precision.

Let's analyze the given statements about confidence intervals (CI) of 99% and 95%:

1. **We have a smaller range of numbers in the 99% confidence interval.**  
   - **False**: As the confidence level increases (from 95% to 99%), the range of the confidence interval increases. The 99% confidence interval will have a **wider range** of numbers compared to the 95% confidence interval.

2. **From 95% to 99% confidence interval, we increase the confidence level.**  
   - **True**: Moving from a 95% confidence interval to a 99% confidence interval means we are increasing the confidence level.

3. **The 99% confidence interval is larger and contains less numbers.**  
   - **False**: The 99% confidence interval is indeed larger (wider), but it **contains more numbers** than the 95% confidence interval. 

4. **From 95% to 99% confidence interval, we lose precision.**  
   - **True**: Increasing the confidence level from 95% to 99% results in a wider interval, meaning the estimate becomes less precise. We are more confident the true value is within the interval, but the interval itself is broader, losing some precision.

### True statements:
- From 95% to 99% confidence interval, we increase the confidence level.
- From 95% to 99% confidence interval, we lose precision.

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Would you like a deeper explanation or examples?

Here are 5 related questions you might consider:

1. How is the margin of error affected by increasing the confidence level?
2. What role does the sample size play in determining the width of a confidence interval?
3. How can you interpret a 99% confidence interval in practical terms?
4. What happens to a confidence interval if the standard deviation increases?
5. Can a smaller sample size lead to a wider confidence interval even at 95%?

**Tip:** As confidence level increases, the trade-off is between **confidence** and **precision**—you gain more confidence but lose precision.

Compare a confidence interval of 99% to 95%. Select all of the below statements that are true. We have a smaller range of numbers in the 99% confidence interval. From 95% to 99% confidence interval, we increase the confidence level. The 99% confidence interval is larger and contains less numbers. From 95% to 99% confidence interval, we lose precision.

Explore the differences between 99% and 95% confidence intervals in statistics. Understand key concepts like the increase in confidence level, the trade-off with precision, and the impact on the range of the interval. Learn with clear examples and detailed explanations, suitable for college-level statistics.

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