Question

Based on an exit poll with a 95% confidence interval (54% +/- 3%), can we confidently state:

a) The senator got a majority of the vote (greater than 50%) and was re-elected.
b) The senator did not get a majority of the vote.
c) The senator's popularity is uncertain.
d) The senator received exactly 54% of the vote.

Answer 1

Based on a 95% confidence interval, we can confidently state whether the senator got a majority of the vote, did not get a majority of the vote, the senator's popularity is uncertain, or the senator received exactly 54% of the vote.

Step-by-step explanation:

To answer this question, we need to understand the concept of confidence intervals. The 95% confidence interval given in the exit poll is 54% +/- 3%. This means that we are 95% confident that the true percentage of votes for the senator falls within the range of 51% to 57%. Based on this information, we can confidently state that:

1. a) The senator got a majority of the vote (greater than 50%) and was re-elected, because 51% is greater than 50%.
2. b) The senator did not get a majority of the vote, because 57% is not less than 50%.
3. c) The senator's popularity is uncertain, because the true percentage could be anywhere between 51% and 57%.
4. d) The senator received exactly 54% of the vote, because the range of the confidence interval is 51% to 57% and does not include exactly 54%.