To determine a likely value for the number of voters who will support the independent candidate, we need to consider the given information:

• Total expected voter turnout: 80,000
• Estimated percentage for the independent candidate: 45%
• Margin of error: ±3.5%

Step-by-Step Solution

1. Calculate the estimated number of voters:

$\text{Estimated Number of Voters} = 80,000 \times 0.45 = 36,000$

2. Determine the range of likely values using the margin of error:

The margin of error is ±3.5%, which means the actual percentage could be as low as $45\% - 3.5\% = 41.5\%$ or as high as $45\% + 3.5\% = 48.5\%$.

3. Calculate the number of voters corresponding to these percentages:

• Lower bound:
  $80,000 \times 0.415 = 33,200$

• Upper bound:
  $80,000 \times 0.485 = 38,800$

Final Answer

A likely value for the total number of voters in the district who will vote for the independent candidate would fall between 33,200 and 38,800.

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Relative Questions:

1. How is the margin of error calculated for polls?
2. What impact does sample size have on the margin of error?
3. How can we determine confidence intervals for voter turnout estimates?
4. What is the probability that the actual percentage falls outside the margin of error?
5. How does changing the total voter turnout affect these calculations?

Tip: Understanding the margin of error is crucial in interpreting poll results accurately. It represents the range within which the true value is expected to fall with a certain confidence level, typically 95%.