Math Problem Statement

Question content area top Part 1 Use the given confidence interval to find the margin of error and the sample proportion. ​(0.694​,0.722​)

Solution

To find the margin of error and the sample proportion from the given confidence interval (0.694,0.722)(0.694, 0.722), we use the following steps:

  1. Margin of Error: The margin of error EE is half the width of the confidence interval.

    E=0.7220.6942=0.0282=0.014E = \frac{0.722 - 0.694}{2} = \frac{0.028}{2} = 0.014

  2. Sample Proportion: The sample proportion p^\hat{p} is the midpoint of the confidence interval.

    p^=0.694+0.7222=1.4162=0.708\hat{p} = \frac{0.694 + 0.722}{2} = \frac{1.416}{2} = 0.708

Answers:

  • Margin of Error (E): 0.0140.014
  • Sample Proportion (p^\hat{p}): 0.7080.708

Would you like more details on these steps or have any questions?

Here are some related questions:

  1. How is the margin of error calculated in a confidence interval?
  2. What is the interpretation of a confidence interval in statistics?
  3. How do you determine the sample proportion from a confidence interval?
  4. What does the sample proportion represent in this context?
  5. How does the sample size affect the margin of error in a confidence interval?

Tip: The confidence interval provides an estimated range for the population parameter, and the margin of error indicates how much the sample proportion might differ from the true population proportion within the given confidence level.

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Math Problem Analysis

Mathematical Concepts

Confidence Interval
Margin of Error
Sample Proportion

Formulas

Margin of Error = (Upper bound - Lower bound) / 2
Sample Proportion = (Upper bound + Lower bound) / 2

Theorems

Confidence Interval Theory
Margin of Error Calculation

Suitable Grade Level

Grades 11-12