Check it out! : Estimating with Confidence

When trying to predict the winner of a major election, it is common for polling companies to ask voters whom they voted for as the voters exit the polling station. These exit poll results are then reported, and predictions about the winner are made well before all of the actual votes have been counted. Commonly, the results are reported along with a margin of error. The results of a particular exit poll are listed in the table on the next slide : Estimating with Confidence

Notice the footnote showing that the margin of error is ±3%. This indicates that the actual election results could be 3% higher (+3%) or 3% lower (–3%) than the reported exit poll results : Estimating with Confidence Exit Poll Results* CandidatePercentage of votes won Archer30% Benton34% Castellano32% *Margin of error: ±3%

1.Based on the exit poll results and a margin of error of ±3%, determine the range that would represent candidate Archer’s results. 2.Based on the exit poll results and a margin of error of ±3%, determine the range that would represent candidate Benton’s results. 3.Based on the exit poll results and a margin of error of ±3%, determine the range that would represent candidate Castellano’s results. 4.Based on your answers for problems 1–3, which candidate do you predict won the election? Explain your answer : Estimating with Confidence

1.Based on the exit poll results and a margin of error of ±3%, determine the range that would represent candidate Archer’s results. According to the table of tallied exit poll responses, Archer won 30% of the vote. The margin of error tells us that this result may be 3% too high, or 3% too low. To determine the range that would represent Archer’s results, you must add 3% to the poll result, and then subtract 3% from the poll result : Estimating with Confidence

To determine the lower bound of the range, subtract 3% from 30%. 30 – 3 = 27 To determine the upper bound of the range, add 3% to 30% = 33 The range that would represent Archer’s results is 27–33%. Archer could have between 27% and 33% of the vote : Estimating with Confidence

2.Based on the exit poll results and a margin of error of ±3%, determine the range that would represent candidate Benton’s results. According to the table, Benton won 34% of the vote. The margin of error tells us that this result may be 3% too high, or 3% too low. To determine the range that would represent Benton’s results, again add 3% to the poll result, and then subtract 3% from the poll result : Estimating with Confidence

To determine the lower bound of the range, subtract 3% from 34%. 34 – 3 = 31 To determine the upper bound of the range, add 3% to 34% = 37 The range that would represent Benton’s results is 31–37%. Benton could have between 31% and 37% of the vote : Estimating with Confidence

3.Based on the exit poll results and a margin of error of ±3%, determine the range that would represent candidate Castellano’s results. According to the table, Castellano won 32% of the vote. The margin of error tells us that this result may be 3% too high, or 3% too low. To determine the range that would represent Castellano’s results, add 3% to the poll result, and then subtract 3% from the poll result : Estimating with Confidence

To determine the lower bound of the range, subtract 3% from 32%. 32 – 3 = 29 To determine the upper bound of the range, add 3% to 32% = 35 The range that would represent Castellano’s results is 29–35%. Castellano could have between 29% and 35% of the vote : Estimating with Confidence

4Based on your answers for problems 1–3, which candidate do you predict won the election? Explain your answer. At first glance, it appears as though Benton won the election. Benton has the highest percentage in the table and the highest upper-bound percentage; however, there are several instances of overlap in the ranges identified. The ranges of all three candidates include the possibility of earning 31%, 32%, and 33% of the vote. While it is likely that Benton won the election, the overlaps in the margins of error make the election too close to call based on these polling results : Estimating with Confidence