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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 percentage of people who said they preferred Candidate A was
80%. The margin of error for the survey was
4%. Write a confidence interval for the percentage of the population that supports Candidate A.

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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 percentage of people who said they preferred Candidate A was $80 \%$ . The margin of error for the survey was $4 \%$ . Write a confidence interval for the percentage of the population that supports Candidate A.

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Interpret confidence intervals for population means

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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 percentage of people who said they preferred Candidate A was

80 \%

. The margin of error for the survey was

4 \%

. Write a confidence interval for the percentage of the population that supports Candidate A.

Understand Confidence Interval: Understand the concept of a confidence interval. A confidence interval gives a range of values within which we can say with a certain level of confidence that the true population parameter lies. In this case, we are looking for the interval around the survey percentage that includes the true percentage of the population that supports Candidate A.
Calculate Lower Bound: Calculate the lower bound of the confidence interval. $\newline$ To find the lower bound, we subtract the margin of error from the survey percentage. $\newline$ Lower bound $= \text{Survey percentage} - \text{Margin of error}$ $\newline$ Lower bound $= 80\% - 4\%$ $\newline$ Lower bound $= 76\%$
Calculate Upper Bound: Calculate the upper bound of the confidence interval. $\newline$ To find the upper bound, we add the margin of error to the survey percentage. $\newline$ Upper bound $= \text{Survey percentage} + \text{Margin of error}$ $\newline$ Upper bound $= 80\% + 4\%$ $\newline$ Upper bound $= 84\%$
Write Confidence Interval: Write the confidence interval. $\newline$ The confidence interval is written as a pair of values, the lower bound and the upper bound. $\newline$ Confidence interval = $(\text{Lower bound}, \text{Upper bound})$ $\newline$ Confidence interval = $(76\%, 84\%)$

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