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A survey was given to a random sample of the residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. The percentage of people who said the supported the plan to raise taxes was
34%. The margin of error for the survey was
4%. Write a confidence interval for the percentage of the population that favors the plan.

A survey was given to a random sample of the residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. The percentage of people who said the supported the plan to raise taxes was $34 \%$ . The margin of error for the survey was $4 \%$ . Write a confidence interval for the percentage of the population that favors the plan. $\newline$ (__ ,_)

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Interpret confidence intervals for population means

Full solution

Q. A survey was given to a random sample of the residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. The percentage of people who said the supported the plan to raise taxes was

34 \%

. The margin of error for the survey was

4 \%

. Write a confidence interval for the percentage of the population that favors the plan.

\newline

(________ ,_______)

Understand Given Information: Understand the given information and what is being asked. $\newline$ We are given the percentage of people who support the plan ( $34\%$ ) and the margin of error ( $4\%$ ). We need to calculate the confidence interval for the population's support percentage.
Calculate Lower Bound: Calculate the lower bound of the confidence interval. $\newline$ To find the lower bound, subtract the margin of error from the percentage of people who support the plan. $\newline$ Lower bound = $34\% - 4\% = 30\%$
Calculate Upper Bound: Calculate the upper bound of the confidence interval. $\newline$ To find the upper bound, add the margin of error to the percentage of people who support the plan. $\newline$ Upper bound = $34\% + 4\% = 38\%$
Write Confidence Interval: Write the confidence interval. $\newline$ The confidence interval is the range from the lower bound to the upper bound. $\newline$ Confidence interval = $[30\%, 38\%]$

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