Question 1126022
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We don't know the true population proportion of people who would vote Republican unless we did a full census of voters of Central Illinois. The next best thing is to do a sample. With a sample, there's usually a tendency to be a bit off the mark. The best guess we have is that "56.8?% would choose the Republican ticket" with some margin of error to help set up the interval. 


56.8% is the midpoint of the interval
The margin of error is 3.8 percentage points
Subtract the midpoint and the margin of error: 56.8% - 3.8% = 53%
Add the midpoint to the margin of error: 56.8% + 3.8% = 60.6%


So the interval spans from 53% to 60.6% which represents the likely window of possible percentages of people who vote Republican. 


The best case scenarios for the Democrats is that the Republican ticket gets 53% of the vote, which means that even in this scenario, they would lose Central Illinois. The only way they would stand a chance is if the percentage dipped below 50%


<b><font color=red size=4>Answer: 53% to 60.6%; Yes</font></b>
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