Questions: A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found a confidence interval for the mean score to be between 433 and 461. What is the margin of error on the survey? Do not write ± on the margin of error.

A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found a confidence interval for the mean score to be between 433 and 461. What is the margin of error on the survey? Do not write ± on the margin of error.
Transcript text: A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found a confidence interval for the mean score to be between 433 and 461. What is the margin of error on the survey? Do not write $\pm$ on the margin of error.
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Solution

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Solution Steps

To find the margin of error for the confidence interval, we need to calculate the difference between the upper limit and the lower limit of the interval, and then divide that difference by 2.

Step 1: Identify the Confidence Interval Limits

The confidence interval for the mean SAT scores is given as between 433 and 461. We denote the lower limit as \( L = 433 \) and the upper limit as \( U = 461 \).

Step 2: Calculate the Margin of Error

The margin of error (ME) is calculated using the formula: \[ \text{ME} = \frac{U - L}{2} \] Substituting the given values: \[ \text{ME} = \frac{461 - 433}{2} = \frac{28}{2} = 14.0 \]

Final Answer

The margin of error is \(\boxed{14.0}\).

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