The problem asks to find the margin of error and sample mean given the confidence interval (13.5, 21.1).

Step 1: Formula for the Sample Mean

The sample mean $\bar{x}$ is the midpoint of the confidence interval: $\bar{x} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}$ Substituting the values: $\bar{x} = \frac{13.5 + 21.1}{2} = \frac{34.6}{2} = 17.3$

Step 2: Formula for the Margin of Error

The margin of error $E$ is half the width of the confidence interval: $E = \frac{\text{Upper Limit} - \text{Lower Limit}}{2}$ Substituting the values: $E = \frac{21.1 - 13.5}{2} = \frac{7.6}{2} = 3.8$

Final Results:

• Sample Mean: $17.3$
• Margin of Error: $3.8$

Let me know if you need further clarification or assistance! Here are five related questions to expand your understanding:

1. What does the margin of error represent in a confidence interval?
2. How is the confidence interval related to the sample mean and margin of error?
3. How would the confidence interval change if the margin of error decreased?
4. How do you calculate the confidence interval if given the sample mean and margin of error?
5. What are the implications of a wider confidence interval in data analysis?

Tip: Always double-check your calculations when dealing with decimals to avoid rounding errors!