Question Hello, If i have a very large bucket of several thousand balls. All I know is that almost all the balls are black and a small percentage are red. If i take out a ball one at a time and note the color. What is the minimum number of balls i need to take out to have an almost certain accuracy of the ratio of black to red balls ?
Im looking for an answer will sound something like: you will need X number of red balls to be 95% sure of the ratio and Y number of red balls to be 99% sure etc.
Thanks !
Answer In order to find sample size you need some rough estimate based on simialr study or polot study, with out these preliminaries you cant find any sample size.Let the proportion of getting red balls be p. If nothing is known we get optimum minimum sample size we get for p=50%=0.5.
In order to get sample size n, the formula is
n=(Zalpha)^2 * p* q/d^2 Here Zalpha =1.96 for 95% confidence (sure) and 2.58 for 99% sure i.e
confidence, d = amount of error tolerable around p, it is usually taken up to 10%, so that your study estimate will be +_10%
Suppose in your case assume 20% balls are red p=0.2,q=0.8,d=0.02,2% error tolearable around p,with 95% sure, the sample size required will be
n =1.96*1.96*0.2*0.8/(0.02*0.02)
=1536.34
You need 1536 balls, for 99% confidence instead of 1.96 take the value of 2.58.
