Certainly! Below is an example of how to explain a **confidence interval** with hypothetical values:

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**Explanation of the Confidence Interval (95% CI: 10.5 to 15.2)**

### **Overview:**
A **confidence interval (CI)** is a range of values that is used to estimate an unknown population parameter. In this case, the interval estimates the **mean** of a population based on sample data, and the 95% confidence level indicates that there is a **95% probability** that the true population mean lies within this range.

### **Given:**
– **Confidence Interval:** 10.5 to 15.2
– **Confidence Level:** 95%

### **Interpretation:**

1. **Meaning of the Confidence Interval:**
The **confidence interval** of **10.5 to 15.2** means that we are **95% confident** that the true population mean falls between **10.5** and **15.2**. This range represents the uncertainty associated with estimating the population mean from the sample data.

2. **Confidence Level:**
The **95% confidence level** implies that if we were to take 100 different samples from the same population, approximately 95 of the resulting confidence intervals would contain the true population mean. It is important to note that the **confidence interval itself** does not change the true value of the population mean; it only represents the range within which that true value is likely to lie, given the sample data.

3. **Statistical Implications:**
– The interval **does not** imply that there is a 95% chance that the true population mean lies within the interval. Rather, it suggests that the estimation procedure will yield intervals containing the true mean 95% of the time across repeated sampling.
– If the interval were to include values both above and below the hypothesized population mean (e.g., zero), this would suggest that there is no significant difference between the sample and the population mean.

4. **Practical Example:**
In a study evaluating the average weight loss of participants on a new diet program, a 95% confidence interval of **10.5 to 15.2 pounds** means that, based on the sample data, the program is expected to result in a mean weight loss within this range. We are 95% confident that the true mean weight loss for the entire population of participants lies between **10.5 pounds and 15.2 pounds**.

### **Conclusion:**
The confidence interval of **10.5 to 15.2** provides an estimate of the population mean, and with a 95% level of confidence, we can be reasonably sure that the true mean lies within this interval. This statistical estimate helps to quantify the uncertainty in sample-based estimates and provides a useful range for decision-making in the context of the analysis.

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This explanation provides a clear, concise interpretation of a confidence interval with a focus on key aspects such as the confidence level, statistical meaning, and practical implications. The structure is designed for clarity and easy understanding.