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Math·Problem-Solving and Data Analysis·Inference from sample statistics and margin of error

easy

For a survey, a sample of $562$ people was selected at random from all registered voters in a county. Based on the survey, it is estimated that $73\%$ of all registered voters in the county are in favor of a new law, with an associated margin of error of $3.67\%$. Which of the following best describes the plausible values for the percent of all registered voters in the county who are in favor of the new law?

A

Any value greater than $69.33\%$ and less than $76.67\%$

B

Any value less than $69.33\%$ or greater than $76.67\%$

C

Any value greater than $69.33\%$

D

Any value less than $76.67\%$