SOLUTION: Following the Republican National​ Convention, a poll of voters in a Central Illinois community showed that 56.8​% would choose the Republican ticket to win over the D

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Question 1126022: Following the Republican National​ Convention, a poll of voters in a Central Illinois community showed that 56.8​% would choose the Republican ticket to win over the Democrat ticket no matter whom the Democrats chose for​ vice-president. The margin of error was 3.8 percentage points. Should the Democrats expect to lose Central​ Illinois?
A.54.9​% to 58.7​%; Yes
B. 49.2​% to 56.8​%; No
C.56.8​% to 60.6​%; Yes
D.53​% to 60.6​%; Yes
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

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%

Answer: 53% to 60.6%; Yes
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