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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
64%. The margin of error for the survey was
3%. Write a confidence interval for the percentage of the population that supports Candidate A.

(◻,◻)

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 $64 \%$ . The margin of error for the survey was $3 \%$ . Write a confidence interval for the percentage of the population that supports Candidate A.

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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 percentage of people who said they preferred Candidate A was

64 \%

. The margin of error for the survey was

3 \%

. 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 range of percentages within which the true support for Candidate A lies, given a margin of error.
Calculate Lower Bound: Calculate the lower bound of the confidence interval. $\newline$ To find the lower bound, subtract the margin of error from the given percentage. $\newline$ Lower bound = $64\% - 3\% = 61\%$
Calculate Upper Bound: Calculate the upper bound of the confidence interval. $\newline$ To find the upper bound, add the margin of error to the given percentage. $\newline$ Upper bound = $64\% + 3\% = 67\%$
Write Confidence Interval: Write the confidence interval. $\newline$ The confidence interval is expressed as $(\text{lower bound}, \text{upper bound})$ . Therefore, the confidence interval for the percentage of the population that supports Candidate A is $(61\%, 67\%)$ .

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