Find the minimum sample size that is required to estimate the proportion within 5% of the true proportion with 98% confidence.
a. 9
b. 8
c. 397
d. 307
Bad question. Needs more information.
Typically, (z^2 * s^2)/(d^2), so (1.96^2) * p*(1-p) / (0.025^2)
To be conserative, [(1.96^2) * (1/2)^2] / (0.025^2)
I was once a consultant in a legal dispute where this was important. The client was asking the wrong people. The entire population that required research was around 500, but it was VERY expensive to research even one case. We needed to know how many to sample to see if we REALLY needed to research EVERY case. The first three people who tried to answer the question said the SMALLER sample had to be OVER 500 - more than the entire population! As this made no sense, they kept looking for the answer. Fortunately, more rational estimates were obtained by the introduction of the Finite Population Correction Factor. 13 or 14 as I recall.