To determine which of the given estimates most likely comes from a small sample based on a [tex]$95\%$[/tex] confidence level, we need to consider the margin of error associated with each estimate. The margin of error gives us an idea of how much the estimate can vary and generally, a larger margin of error is indicative of a smaller sample size.
Here are the estimates with their corresponding margins of error:
- A: [tex]\( 62\% (\pm 6\%) \)[/tex]
- B: [tex]\( 60\% (\pm 18\%) \)[/tex]
- C: [tex]\( 71\% (\pm 4\%) \)[/tex]
- D: [tex]\( 65\% (\pm 2\%) \)[/tex]
1. For option A, the margin of error is [tex]\( \pm 6\% \)[/tex].
2. For option B, the margin of error is [tex]\( \pm 18\% \)[/tex].
3. For option C, the margin of error is [tex]\( \pm 4\% \)[/tex].
4. For option D, the margin of error is [tex]\( \pm 2\% \)[/tex].
A larger margin of error indicates that the estimates are more spread out and therefore are more uncertain. This uncertainty is usually due to a smaller sample size, as larger samples tend to give more precise (i.e., with smaller margin of error) estimates.
Now let's compare the margins of error:
- Option A: [tex]\( 6\% \)[/tex]
- Option B: [tex]\( 18\% \)[/tex]
- Option C: [tex]\( 4\% \)[/tex]
- Option D: [tex]\( 2\% \)[/tex]
The largest margin of error among these is [tex]\( 18\% \)[/tex], which corresponds to option B.
Hence, the estimate [tex]\( 60\% (\pm 18\%) \)[/tex] under option B most likely comes from a small sample.
