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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 501 and 531 . What is the margin of error on the survey? Do not write
+- on the margin of error.
Answer:____-

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 $501$ and $531$ . What is the margin of error on the survey? Do not write $\pm$ on the margin of error. $\newline$ Answer:________

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Interpret confidence intervals for population means

Full solution

Q. 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

501

and

531

. What is the margin of error on the survey? Do not write

\pm

on the margin of error.

\newline

Answer:________

Calculate Confidence Interval: The confidence interval for the mean score is given as between $501$ and $531$ . To find the margin of error, we need to calculate the distance from the mean to one end of the confidence interval.
Calculate Mean: The mean (average) of the confidence interval is the midpoint between $501$ and $531$ . We calculate this by adding the two values together and dividing by $2$ . $\newline$ Mean = $(501 + 531) / 2$ $\newline$ Mean = $1032 / 2$ $\newline$ Mean = $516$
Calculate Margin of Error: Now that we have the mean, we can calculate the margin of error by subtracting the lower bound of the confidence interval from the mean. $\newline$ Margin of error = Mean - Lower bound $\newline$ Margin of error = $516 - 501$ $\newline$ Margin of error = $15$

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