Questions: A poll conducted a week before the school election to the student council showed that Janice would win with 63% of the vote. The margin of error was 14%. If Janice needs to receive at least half the votes to win the election, can we be confident of Janice's victory? Yes, because the poll stated that she will win with 63% of the vote. No, because she could receive as low as 14% of the vote. No, because she could receive as low as 49% of the vote. Yes, because she could receive as much as 77% of the vote.

A poll conducted a week before the school election to the student council showed that Janice would win with 63% of the vote. The margin of error was 14%. If Janice needs to receive at least half the votes to win the election, can we be confident of Janice's victory? Yes, because the poll stated that she will win with 63% of the vote. No, because she could receive as low as 14% of the vote. No, because she could receive as low as 49% of the vote. Yes, because she could receive as much as 77% of the vote.
Transcript text: A poll conducted a week before the school election to the student council showed that Janice would win with $63 \%$ of the vote. The margin of error was $14 \%$. If Janice needs to receive at least half the votes to win the election, can we be confident of Janice's victory? Yes, because the poll stated that she will win with $63 \%$ of the vote. No, because she could receive as low as $14 \%$ of the vote. No, because she could receive as low as $49 \%$ of the vote. Yes, because she could receive as much as $77 \%$ of the vote.
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Solution

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Solution Steps

To determine if we can be confident of Janice's victory, we need to consider the margin of error. The margin of error indicates the range within which the true percentage of votes Janice might receive lies. We will calculate the lower and upper bounds of this range and check if the lower bound is still above 50%.

Step 1: Calculate the Lower Bound

To determine the lower bound of the percentage of votes Janice might receive, we subtract the margin of error from the poll percentage: \[ \text{Lower Bound} = 63\% - 14\% = 49\% \]

Step 2: Calculate the Upper Bound

To determine the upper bound of the percentage of votes Janice might receive, we add the margin of error to the poll percentage: \[ \text{Upper Bound} = 63\% + 14\% = 77\% \]

Step 3: Determine Confidence in Janice's Victory

Janice needs to receive at least 50% of the votes to win the election. We check if the lower bound is greater than or equal to 50%: \[ 49\% < 50\% \] Since the lower bound is less than 50%, we cannot be confident that Janice will win the election.

Final Answer

\(\boxed{\text{No, because she could receive as low as 49\% of the vote.}}\)

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