To determine the margin of error for the given confidence interval expression:
[tex]\[
\left( \bar{x}_1 - \bar{x}_2 \right) \pm 2 (se)
\][/tex]
Let’s break this down step-by-step.
1. Identify Components:
- [tex]\(\bar{x}_1\)[/tex] and [tex]\(\bar{x}_2\)[/tex] are the sample means of two groups.
- [tex]\(se\)[/tex] represents the standard error of the difference between these two sample means.
- The [tex]\( \pm \)[/tex] symbol indicates the range within which the true difference is expected to fall, given a certain level of confidence.
2. Understand the Confidence Interval:
The confidence interval is expressed as:
[tex]\[
\left( \bar{x}_1 - \bar{x}_2 \right) \pm 2 (se)
\][/tex]
Here, the term [tex]\(2(se)\)[/tex] represents the interval range on either side of the sample mean difference [tex]\(\left( \bar{x}_1 - \bar{x}_2 \right)\)[/tex].
3. Determine the Margin of Error:
The margin of error specifies the distance from the sample mean difference to the bounds of the confidence interval. This distance is captured by the term following the plus-minus symbol ([tex]\(\pm\)[/tex]) in the interval expression:
[tex]\[
2 (se)
\][/tex]
This implies that the margin of error is [tex]\(2 \times\)[/tex] the standard error ([tex]\(se\)[/tex]).
4. Conclusion:
Since the question specifically asks for the margin of error (not the standard error itself), it is given directly by [tex]\(2 \times (se)\)[/tex], hence the margin of error is:
[tex]\[
\boxed{2}
\][/tex]
