To find the margin of error (E) and the sample proportion (p̂), we can use the provided confidence interval (0.708, 0.734).

Step 1: Sample Proportion (p̂)

The sample proportion $\hat{p}$ is the midpoint of the confidence interval.

$\hat{p} = \frac{0.708 + 0.734}{2} = 0.721$

Step 2: Margin of Error (E)

The margin of error (E) is the difference between the upper limit of the confidence interval and the sample proportion.

$E = 0.734 - 0.721 = 0.013$

Results:

• Margin of error (E) = 0.013
• Sample proportion (p̂) = 0.721

Let me know if you would like further details or have any additional questions!

Follow-up Questions:

1. How is the margin of error useful in interpreting confidence intervals?
2. What does a higher sample size do to the margin of error?
3. How would you calculate the confidence interval if you had the margin of error and the sample proportion?
4. What assumptions are made when calculating a confidence interval?
5. How does the confidence level affect the width of the confidence interval?

Tip:

When interpreting confidence intervals, remember that the margin of error gives you a range of uncertainty around the sample proportion, and the true population proportion is expected to lie within this interval with the given confidence level.