To determine which of the estimates most likely comes from a small sample, we need to compare the margins of error associated with each estimate at a [tex]$95\%$[/tex] confidence level. A larger margin of error generally indicates that the estimate was derived from a smaller sample size.
Let's examine the given estimates:
- Estimate A: [tex]\(65\%\)[/tex] with a margin of error of [tex]\(\pm 2\%\)[/tex]
- Estimate B: [tex]\(60\%\)[/tex] with a margin of error of [tex]\(\pm 18\%\)[/tex]
- Estimate C: [tex]\(62\%\)[/tex] with a margin of error of [tex]\(\pm 6\%\)[/tex]
- Estimate D: [tex]\(71\%\)[/tex] with a margin of error of [tex]\(\pm 4\%\)[/tex]
Here are the margins of error:
- Margin of error for Estimate A: [tex]\(2\%\)[/tex]
- Margin of error for Estimate B: [tex]\(18\%\)[/tex]
- Margin of error for Estimate C: [tex]\(6\%\)[/tex]
- Margin of error for Estimate D: [tex]\(4\%\)[/tex]
The larger the margin of error, the more likely it is that the estimate comes from a smaller sample. Comparing the margins of error, it is clear that:
- [tex]\(2\%\)[/tex] is the smallest margin.
- [tex]\(18\%\)[/tex] is the largest margin.
- [tex]\(6\%\)[/tex] and [tex]\(4\%\)[/tex] are intermediate margins.
Thus, the margin of error of [tex]\(\pm 18\%\)[/tex] is the largest among the given estimates. Therefore, the estimate:
- Estimate B: [tex]\(60\%\)[/tex] with a margin of error of [tex]\(\pm 18\%\)[/tex],
is most likely to come from a small sample.
So, the answer is:
B. [tex]\(60\%\)[/tex] ( [tex]\(\pm 18\%\)[/tex] )
