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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
69%. The margin of error for the survey was
2%. 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 $69 \%$ . The margin of error for the survey was $2 \%$ . Write a confidence interval for the percentage of the population that supports Candidate A. $\newline$ (,)

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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

69 \%

. The margin of error for the survey was

2 \%

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

\newline

(______,______)

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. The margin of error is the amount that is added to and subtracted from the point estimate (in this case, the percentage of people who prefer Candidate A) to create the interval.
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 said they preferred Candidate A. $\newline$ Lower bound = $69\% - 2\% = 67\%$
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 said they preferred Candidate A. $\newline$ Upper bound = $69\% + 2\% = 71\%$
Write Confidence Interval: Write the confidence interval. $\newline$ The confidence interval is expressed as $(\text{lower bound}, \text{upper bound})$ . From the calculations in Step $2$ and Step $3$ , the confidence interval is $(67\%, 71\%)$ .

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