1.6.3 Quiz: Evaluating Published Reports

Question 1 of 10:

Which of the following estimates at a [tex]$95 \%$[/tex] confidence level most likely comes from a small sample?

A. [tex]$71 \% (\pm 6 \%)$[/tex]
B. [tex]$60 \% (\pm 4 \%)$[/tex]
C. [tex]$62 \% (\pm 18 \%)$[/tex]
D. [tex]$65 \% (\pm 2 \%)$[/tex]



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]