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A survey was given to a random sample of voters in the United States to ask about their preference for a presidential candidate. The survey reported a confidence interval that between
65.5% and
72.5% of the population preferred Candidate A. What is the margin of error on the survey? Do not write
+- on the margin of error.
Answer:____

A survey was given to a random sample of voters in the United States to ask about their preference for a presidential candidate. The survey reported a confidence interval that between $65.5 \%$ and $72.5 \%$ of the population preferred Candidate A. 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 survey was given to a random sample of voters in the United States to ask about their preference for a presidential candidate. The survey reported a confidence interval that between

65.5 \%

and

72.5 \%

of the population preferred Candidate A. What is the margin of error on the survey? Do not write

\pm

on the margin of error.

\newline

Answer:_____-

Understand Margin of Error: Understand the concept of margin of error. The margin of error in a confidence interval for a survey is the range that the true population parameter is expected to fall within. It is calculated as the difference between the upper value and the point estimate or the point estimate and the lower value of the confidence interval.
Calculate Midpoint: Calculate the midpoint of the confidence interval. $\newline$ To find the margin of error, we first need to calculate the midpoint of the confidence interval, which serves as our point estimate. The midpoint is the average of the lower and upper bounds of the confidence interval. $\newline$ Midpoint = $(\text{Lower Bound} + \text{Upper Bound}) / 2$ $\newline$ Midpoint = $(65.5\% + 72.5\%) / 2$ $\newline$ Midpoint = $138\% / 2$ $\newline$ Midpoint = $69\%$
Calculate Margin of Error: Calculate the margin of error. $\newline$ The margin of error is the difference between the upper bound and the midpoint or the midpoint and the lower bound. $\newline$ Margin of Error = Upper Bound - Midpoint $\newline$ Margin of Error = $72.5\% - 69\%$ $\newline$ Margin of Error = $3.5\%$

More problems from Interpret confidence intervals for population means

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