Math Problem Statement

The mean was found to be 23% and the confidence interval was (19.7%,26.3%) therefore the margin of error was +/- _____%.

Solution

The margin of error (ME) can be found by calculating the difference between the mean and one of the bounds of the confidence interval.

Given:

  • Mean = 23%
  • Confidence Interval = (19.7%, 26.3%)

The margin of error is calculated as:

Margin of Error=Upper BoundMean or MeanLower Bound\text{Margin of Error} = \text{Upper Bound} - \text{Mean} \text{ or } \text{Mean} - \text{Lower Bound}

Let's calculate:

Margin of Error=23%19.7%=3.3%\text{Margin of Error} = 23\% - 19.7\% = 3.3\%

Or:

Margin of Error=26.3%23%=3.3%\text{Margin of Error} = 26.3\% - 23\% = 3.3\%

Thus, the margin of error is ±3.3%.

Would you like more details, or do you have any questions?

Here are 5 related questions you might consider:

  1. How is the confidence interval interpreted in terms of population parameters?
  2. What is the significance of a 95% confidence level in confidence intervals?
  3. How do sample size and variability affect the margin of error?
  4. How can you decrease the margin of error in a study?
  5. What is the difference between a one-sided and a two-sided confidence interval?

Tip: The margin of error decreases as the sample size increases, which is why larger studies tend to produce more precise estimates.

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Math Problem Analysis

Mathematical Concepts

Statistics
Confidence Intervals
Margin of Error

Formulas

Margin of Error = Upper Bound - Mean or Mean - Lower Bound

Theorems

Confidence Interval Theorem

Suitable Grade Level

Grades 10-12