Statistics: Sample Size & Error

Hi guys!

I've been reading this board for some time, and finally had a question... we're doing a really simple statistics analysis in regards to business law cases and what the outcomes were. Here's the info... 600 total cases surveyed, found 480 (or 80%) were true in our findings. We want to know if 600 is an adequate sample size to base this off of. In our notes, we were also given a statement of "we are willing to accept this 80% as 3% (or .03) of the true proportion." This is where we get thrown off a little. This is all based on a 90% confidence interval as well.

Can anyone shine some insight on this? Logically, if I understand this correctly, if its only denoted as 3% of the true proportion, than we would need to look at more cases. However, I'm thinking that were gonna need to compute the standard error to find out with a 90% confidence that this an adequate sample.

I really appreciate all your help!!

Marc

Using the normal approximation to the binomial, the margin of error is \(\displaystyle E = 1.645*\sqrt{.8*.2/600} = 0.027\), or about 3 percent. So a sample size of 600 is consistent with this result. That assumes that you want your confidence interval to be within 2.7 percentage points of the true proportion with 90 percent confidence.