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What is the margin of error for this confidence interval?

The [tex]\(95\%\)[/tex] confidence interval for the true difference (post-debate minus pre-debate) in proportions of likely voters who would vote for a candidate was [tex]\((-0.014, 0.064)\)[/tex].

A. [tex]\(\frac{0.064 + (-0.014)}{2} = 0.025\)[/tex]
B. [tex]\(\frac{0.064 - (-0.014)}{2} = 0.039\)[/tex]
C. [tex]\(0.064 + (-0.014) = 0.050\)[/tex]
D. [tex]\(0.064 - (-0.014) = 0.078\)[/tex]



Answer :

GinnyAnswer
To determine the margin of error for the given confidence interval, follow these steps:

1. Identify the confidence interval: The provided confidence interval for the true difference in proportions of likely voters is from [tex]\(-0.014\)[/tex] to [tex]\(0.064\)[/tex].

2. Understand the confidence interval: The margin of error is the measure of the extent of the interval from the center point (midpoint) to either endpoint. It indicates the range within which the true difference in proportions is likely to fall.

3. Calculate the margin of error:

- First, calculate the difference between the upper bound and the lower bound of the confidence interval:
[tex]\[ 0.064 - (-0.014) \][/tex]
- Simplify the subtraction:
[tex]\[ 0.064 + 0.014 = 0.078 \][/tex]

4. Find the margin of error:
- The margin of error is half the width of the confidence interval:
[tex]\[ \frac{0.078}{2} = 0.039 \][/tex]

Therefore, the margin of error for this confidence interval is [tex]\(0.039\)[/tex].

Thus, the correct option is:
[tex]\[ \boxed{\frac{0.064-(-0.014)}{2}=0.039} \][/tex]

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