Math Problem Statement

The mean was found to be 38% and the confidence interval was (34.2%,41.8%) therefore the margin of error was +/- _____%.

Solution

The margin of error (ME) is calculated as half the width of the confidence interval. To find the margin of error, you subtract the lower bound of the interval from the upper bound and divide by 2.

Given:

  • Confidence interval: (34.2%, 41.8%)

Margin of Error Calculation:

Margin of Error=41.8%34.2%2\text{Margin of Error} = \frac{41.8\% - 34.2\%}{2}

Let's calculate this:

Margin of Error=7.6%2=3.8%\text{Margin of Error} = \frac{7.6\%}{2} = 3.8\%

Therefore, the margin of error is ±3.8%.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

  1. How do you interpret a confidence interval in the context of survey results?
  2. What does a larger margin of error indicate about a survey or experiment?
  3. How can you decrease the margin of error in a statistical study?
  4. How does sample size affect the confidence interval and margin of error?
  5. What is the significance level, and how does it relate to confidence intervals?

Tip: A smaller margin of error suggests more precise estimates, often achieved with larger sample sizes or reduced variability in data.

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Math Problem Analysis

Mathematical Concepts

Statistics
Confidence Intervals
Margin of Error

Formulas

Margin of Error = (Upper Bound - Lower Bound) / 2

Theorems

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Suitable Grade Level

Grades 9-12