Which of the following estimates at a 95 confidence level mo

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

Solution

Margin of error = Critical value of z for 95% confidence level*Standard error of p
Standard error of p = sqrt [p*(1-p)/n]

as sample size n is small standard error of p is large giving larger margin of error

Out of the given options smaller the samlple size larger the marigin, so option B 59% (+/- 21%