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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 519 and 557 . 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 $519$ and $557$ . 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

519

and

557

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

\pm

on the margin of error.

\newline

Answer:_______

Understand concept: Understand the concept of a confidence interval and margin of error. The confidence interval gives a range within which the true mean is expected to lie. The margin of error is the amount added to and subtracted from the point estimate (like the sample mean) to create the confidence interval.
Identify bounds: Identify the lower and upper bounds of the confidence interval. $\newline$ The confidence interval is given as between $519$ and $557$ . $\newline$ Lower bound = $519$ $\newline$ Upper bound = $557$
Calculate point estimate: Calculate the point estimate (mean) of the confidence interval. $\newline$ The point estimate is the midpoint of the confidence interval. $\newline$ Point estimate (mean) = $(\text{Lower bound} + \text{Upper bound}) / 2$ $\newline$ Point estimate (mean) = $(519 + 557) / 2$ $\newline$ Point estimate (mean) = $1076 / 2$ $\newline$ Point estimate (mean) = $538$
Calculate margin of error: Calculate the margin of error. $\newline$ The margin of error is the difference between the point estimate and one of the bounds of the confidence interval. $\newline$ Margin of error = Upper bound - Point estimate $\newline$ Margin of error = $557 - 538$ $\newline$ Margin of error = $19$

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