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A survey was given to a random sample of the residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. The percentage of people who said they favored the plan was 35%. The margin of error for the survey was 3%. Which of the following is a reasonable value for the actual percentage of the residents that support the tax plan? 32.4% 39.4% 30.8% 38.8%

A survey was given to a random sample of the residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. The percentage of people who said they favored the plan was 35% 35 \% . The margin of error for the survey was 3% 3 \% . Which of the following is a reasonable value for the actual percentage of the residents that support the tax plan?\newline32.4% 32.4 \% \newline39.4% 39.4 \% \newline30.8% 30.8 \% \newline38.8% 38.8 \%

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Q. A survey was given to a random sample of the residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. The percentage of people who said they favored the plan was 35% 35 \% . The margin of error for the survey was 3% 3 \% . Which of the following is a reasonable value for the actual percentage of the residents that support the tax plan?\newline32.4% 32.4 \% \newline39.4% 39.4 \% \newline30.8% 30.8 \% \newline38.8% 38.8 \%
  1. Understand Margin of Error: Understand the concept of margin of error. The margin of error in a survey gives us a range in which the true value is likely to fall. In this case, the margin of error is 3%3\%. This means that the actual percentage of residents who support the tax plan could be 3%3\% higher or 3%3\% lower than the reported 35%35\%.
  2. Calculate Lower End: Calculate the lower end of the margin of error.\newlineTo find the lower end of the range, we subtract the margin of error from the reported percentage.\newline35%−3%=32%35\% - 3\% = 32\%
  3. Calculate Upper End: Calculate the upper end of the margin of error.\newlineTo find the upper end of the range, we add the margin of error to the reported percentage.\newline35%+3%=38%35\% + 3\% = 38\%
  4. Determine Reasonable Values: Determine the reasonable values for the actual percentage. The reasonable values for the actual percentage of residents that support the tax plan would fall between 32%32\% and 38%38\%. Therefore, any value outside this range would not be considered reasonable given the margin of error.
  5. Compare with Options: Compare the given options with the calculated range.\newlineWe have the following options:\newline- 32.4%32.4\%\newline- 39.4%39.4\%\newline- 30.8%30.8\%\newline- 38.8%38.8\%\newlineWe can see that 32.4%32.4\% and 38.8%38.8\% fall within the range of 32%32\% to 38%38\%, while 39.4%39.4\% and 30.8%30.8\% do not.

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