To solve this problem, we will calculate the margin of error and sample mean from the given confidence interval $(1.66, 1.90)$:

Step 1: Formula for Margin of Error

The margin of error ($E$) is half the width of the confidence interval: $E = \frac{\text{Upper limit} - \text{Lower limit}}{2}$ $E = \frac{1.90 - 1.66}{2} = \frac{0.24}{2} = 0.12$

Step 2: Formula for Sample Mean

The sample mean ($\bar{x}$) is the midpoint of the confidence interval: $\bar{x} = \frac{\text{Upper limit} + \text{Lower limit}}{2}$ $\bar{x} = \frac{1.90 + 1.66}{2} = \frac{3.56}{2} = 1.78$

Final Answers:

• Margin of Error: $0.12$
• Sample Mean: $1.78$

If you need further explanation or assistance with similar problems, feel free to ask!

Related Questions:

1. How is the margin of error affected by the confidence level?
2. What are common methods to calculate a confidence interval?
3. How do you determine if a confidence interval is accurate in real-life scenarios?
4. What role does sample size play in determining the width of a confidence interval?
5. How does increasing the sample size impact the margin of error?

Tip:

Always ensure the confidence interval values (lower and upper limits) are accurate before performing calculations.