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?

correct answer(s)

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

Explanation:

Analyze the poll data and margin of error

• Support for the bond: \(52\%\) with a \(3\%\) margin of error yields a confidence interval of \([49\%, 55\%]\).
• Opposition to the bond: \(47\%\) with a \(3\%\) margin of error yields a confidence interval of \([44\%, 50\%]\).

Determine the statistical overlap

• The confidence intervals for support \([49\%, 55\%]\) and opposition \([44\%, 50\%]\) overlap between \(49\%\) and \(50\%\).
• Because of this overlap, the true support could be below \(50\%\) (e.g., \(49\%\)) and the true opposition could be at or above \(50\%\) (e.g., \(50\%\)).

Evaluate the options

• "The local bond could either pass or not pass in this election as the result is within the margin of error" is correct because the intervals overlap and cross the \(50\%\) threshold.
• "Five percent of the voters in the poll remain undecided" is incorrect (the poll states \(1\%\) were unsure).
• "The local bond is projected to lose" and "The local bond is projected to pass" are too definitive given the statistical overlap.

Answer:

• 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 lose.
• The local bond is projected to pass.