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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
47.5% and
50.5% 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 $47.5 \%$ and $50.5 \%$ of the population preferred Candidate A. $\newline$ 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

47.5 \%

and

50.5 \%

of the population preferred Candidate A.

\newline

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

\pm

on the margin of error.

\newline

Answer:________

Concept of Margin of Error: Understand the concept of margin of error. The margin of error in a confidence interval is the range of values below and above the sample statistic in a confidence interval. It is calculated as the difference between the upper bound and the point estimate or the point estimate and the lower bound of the confidence interval.
Identify Bounds: Identify the upper and lower bounds of the confidence interval. $\newline$ The survey reported that between $47.5\%$ and $50.5\%$ of the population preferred Candidate A. Therefore, the lower bound is $47.5\%$ and the upper bound is $50.5\%$ .
Calculate Point Estimate: Calculate the point estimate. $\newline$ The point estimate is the middle value of the confidence interval. To find it, we average the upper and lower bounds. $\newline$ Point estimate = $(\text{Lower bound} + \text{Upper bound}) / 2$ $\newline$ Point estimate = $(47.5\% + 50.5\%) / 2$ $\newline$ Point estimate = $98\% / 2$ $\newline$ Point estimate = $49\%$
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. Since the point estimate is equidistant from both bounds, we can subtract the lower bound from the point estimate or vice versa. $\newline$ Margin of error = Upper bound - Point estimate $\newline$ Margin of error = $50.5\% - 49\%$ $\newline$ Margin of error = $1.5\%$

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