A group conducted a poll of 2083 likely voters just prior to an election. The results of the survey indicated that candidate A w

Question

3 years ago

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A group conducted a poll of 2083 likely voters just prior to an election. The results of the survey indicated that candidate A w

ould receive 47% of the popular vote and candidate B would receive 44% of the popular vote. The margin of error was reported to be 3%. The group reported that the race was too close to call. Use the concept of a confidence interval to explain what this means. What does it mean to say the race was too close to call?

Mathematics

1 answer:

mart [117] · Answer 1 · 2022-01-05T14:36:38+03:00

Answer:

With the given margin of error its is possible that candidate A wins and candidate B loses, and it is also possible that candidate B wins and candidate A loses. Therefore, the poll cannot predict the winner and this is why race was too close to call a winner.

Step-by-step explanation:

A group conducted a poll of 2083 likely voters.

The results of poll indicate candidate A would receive 47% of the popular vote and and candidate B would receive 44% of the popular vote.

The margin of error was reported to be 3%

So we are given two proportions;

A = 47%

B = 44%

Margin of Error = 3%

The margin of error shows by how many percentage points the results can deviate from the real proportion.

Case I:

A = 47% + 3% = 50%

B = 44% - 3% = 41%

Candidate A wins

Case II:

A = 47% - 3% = 44%

B = 44% + 3% = 47%

Candidate B wins

As you can see, with the given margin of error its is possible that candidate A wins and candidate B loses, and it is also possible that candidate B wins and candidate A loses. Therefore, the poll cannot predict the winner and this is why race was too close to call a winner.