Answer :
To determine which of the given estimates at a 95% confidence level most likely comes from a small sample, we need to consider the margin of error. The margin of error in a confidence interval is influenced by the sample size: smaller sample sizes generally result in larger margins of error.
Let's analyze the given options:
A. \( 71\% (\pm 6\%) \)
- Margin of error: 6%
B. \( 60\% (\pm 4\%) \)
- Margin of error: 4%
C. \( 62\% (\pm 18\%) \)
- Margin of error: 18%
D. \( 65\% (\pm 2\%) \)
- Margin of error: 2%
When comparing the margins of error, we observe that the largest margin of error is 18%, which is associated with option C (\( 62\% (\pm 18\%) \)). A larger margin of error often indicates a smaller sample size because the estimation is less precise.
Therefore, the estimate at a 95% confidence level that most likely comes from a small sample is:
C. [tex]\( 62\% (\pm 18\%) \)[/tex]
Let's analyze the given options:
A. \( 71\% (\pm 6\%) \)
- Margin of error: 6%
B. \( 60\% (\pm 4\%) \)
- Margin of error: 4%
C. \( 62\% (\pm 18\%) \)
- Margin of error: 18%
D. \( 65\% (\pm 2\%) \)
- Margin of error: 2%
When comparing the margins of error, we observe that the largest margin of error is 18%, which is associated with option C (\( 62\% (\pm 18\%) \)). A larger margin of error often indicates a smaller sample size because the estimation is less precise.
Therefore, the estimate at a 95% confidence level that most likely comes from a small sample is:
C. [tex]\( 62\% (\pm 18\%) \)[/tex]
