In a random survey of US adults, a political scientist found that $56 \%$ of the survey respondents are confident in the current administration's ability to make good foreign policy decisions. The margin of error for this estimation is $1 \%$ . Based on this information, which of the following is the most appropriate conclusion? $\newline$ Choose $1$ answer: $\newline$ (A) Exactly $56 \%$ of US adults are confident that $99 \%$ of the foreign policy decisions made by the current administration will be good. $\newline$ (B) The political scientist is $99 \%$ sure that $56 \%$ of the foreign policy decisions made by the current administration will be good ones. $\newline$ (C) Most US adults believe that $55 \%$ to $57 \%$ of the foreign policy decisions made by the current administration will be good ones. $\newline$ (D) It is likely that $55 \%$ to $57 \%$ of all US adults are confident in the current administration's ability to make good foreign policy decisions.

View step-by-step help

Home

Math Problems

Precalculus

Interpret confidence intervals for population means

Full solution

Q. In a random survey of US adults, a political scientist found that

56 \%

of the survey respondents are confident in the current administration's ability to make good foreign policy decisions. The margin of error for this estimation is

1 \%

. Based on this information, which of the following is the most appropriate conclusion?

\newline

Choose

1

answer:

\newline

(A) Exactly

56 \%

of US adults are confident that

99 \%

of the foreign policy decisions made by the current administration will be good.

\newline

(B) The political scientist is

99 \%

sure that

56 \%

of the foreign policy decisions made by the current administration will be good ones.

\newline

55 \%

57 \%

of the foreign policy decisions made by the current administration will be good ones.

\newline

(D) It is likely that

55 \%

57 \%

of all US adults are confident in the current administration's ability to make good foreign policy decisions.

Survey Confidence Percentage: The survey says $56\%$ of respondents are confident in the administration's ability to make good foreign policy decisions, with a margin of error of $1\%$ .
Margin of Error: The margin of error means the actual percentage could be $1\%$ higher or lower than the reported $56\%$ , so it could be between $55\%$ and $57\%$ .
Option (A) Explanation: Option (A) is incorrect because it misinterprets the percentage as a prediction of the success rate of foreign policy decisions.
Option (B) Explanation: Option (B) is incorrect because it confuses the confidence level of the survey with the success rate of the decisions.
Option (C) Explanation: Option (C) is incorrect because it suggests that most US adults believe a specific percentage of decisions will be good, which is not what the survey measures.
Option (D) Explanation: Option (D) correctly interprets the margin of error and the percentage of US adults confident in the administration's ability to make good foreign policy decisions.