Which of the following estimates at a 95% confidence level most likely comes from a small sample?

A. 48% (±21%)
B. 59% (±5%)
C. 67% (±7%)
D. 53% (±3%)

Question

Which of the following estimates at a 95% confidence level most likely comes from a small sample?

 		A.	48% (±21%)
 		B.	59% (±5%)
 		C.	67% (±7%)
 		D.	53% (±3%)

anonymous · Answer

Margin of error = Critical value of z for 95% confidence level*Standard error of p 
Standard error of p = sqrt [p*(1-p)/n] 
Smaller the sample size larger is the standard error of p and margin of error because the confidence coefficient and p value remains the same. 
Therefore, 93% (+/- 24%) is the answer.
 paramvenu · 2 years ago

amistre64 · Answer

small sample sizes result in the biggest margins of error.

amistre64 · Answer

logically,  we would expect a sample size of 5 out of 1000 to not be that representative of the population, and have the biggest error associated with it

whereas, a sample size of 995 out of 1000 is pretty much the population as a whole, and we would expect it to mirror the population parameters almost to a tee.