Question

a random sample of 1,000 americans were polled on a local bond that would fund projects for the school district. the poll results showed that 47 percent of the respondents opposed the bond, 52 percent supported the bond, and 1 percent were unsure. the poll had a 3 percent margin of error.

what can one conclude from this poll?

• the local bond is projected to lose.
• the local bond could either pass or not pass in this election as the result is within the margin of error.
• five percent of the voters in the poll remain undecided.
• the local bond is projected to pass.

Explanation:

Analyze the poll data and margin of error

The poll shows:

• Support for the bond: \(52\%\)
• Opposition to the bond: \(47\%\)
• Unsure: \(1\%\)
• Margin of error: \(\pm 3\%\)

Calculate the confidence intervals

Applying the \(\pm 3\%\) margin of error to the results:

• True support range: \(52\% - 3\% = 49\%\) to \(52\% + 3\% = 55\%\)
• True opposition range: \(47\% - 3\% = 44\%\) to \(47\% + 3\% = 50\%\)

Determine the correct conclusion

Because the confidence intervals overlap (support can be as low as \(49\%\) and opposition can be as high as \(50\%\)), the outcome of the election cannot be definitively projected. Therefore, the bond could either pass or not pass.

Answer:

• The local bond is projected to lose.
• The local bond could either pass or not pass in this election as the result is within the margin of error. (Correct answer)
• Five percent of the voters in the poll remain undecided.
• The local bond is projected to pass.