As a former tutor of elementary statistics (among other mathematics and physical science things) at a local junior college for almost twenty years, I could not resist chiming in on this. If you are talking about human subjects, things can get really complicated. The wording of the question, how you obtain your sample, and a lot of other things can affect the results. None of us has time to go into all the issues involved in that, such as how to detect bias of different kinds in your sample and what are the possible ambiguities in the ways the question is worded. Some of the other respondents have posted responses addressing some of these issues.

If this subject interests anyone here, a good nonmathematical introduction to the subject is _How to Lie with Statistics_ by Darrell Huff, a book that is still in print after several decades. Don't be put off by the age of the examples taken from a time when $25,000 was considered an upper-class, or at least an upper-middle class, income and ten cents might be enough to buy a loaf of bread or a quart of milk.

In our present example, our sample is the the responses from the Ugly Hedgehog members who have volunteered to answer the survey question in a form that will be counted. I won't address here how well the sample represents the intended population because I don't really know what the intended population is. I also assume that any biases in the sample are small enough to be ignored.

There is also a difference between a confidence LEVEL and a confidence INTERVAL The confidence LEVEL is typically used to answer a yes-or-no question of the form, "Is the value we got different enough from the one we would expect from the one we would expect from the null hypotheses (i.e., the result we would expect if the effect we are looking for were absent) to say with enough confidence (defined by the confidence level) to report a positive result?" A confidence INTERVAL is defined usually by two numbers defining 5the limits bounds around our nominal result where we can say that the true result lies, with a confidence determined by the confidence level.

Now let's get down to the problem in front of us, or at least a related problem. I do not have the actual numbers in front of me, so I will make do with approximations. We have three possible results, so I will change the problem to compute a binary result instead: the approximate probability that an individual will answer RAW, which I believe happened with a probability of approximately 40 percent (or p = .40) and that the current count of data points is now around 500 (n = 500). The number of people who answered RAW would therefore be np, or 200. The number q is the probability that a given person answered one of the legal responses other than RAW. The standard deviation for p we shall call s, which is sqrt ((p * q) / n), or sqrt (( 0.40 * 0.60) / 500) = sqrt (0.000480) = 0.0219. To obtain a confidence interval of 98%, we must add and subtract 2.326 times s, or 0.0510, to get the bounds for the confidence interval. In other words, we are 98 percent certain that the actual probability for our hypothetical run will be between p - 0.0510 and p + 0.0510, or 0.349 to 0.451

Of course, this is only an approximation. To get a more exact number, you must use the actual numbers from your own data to get n, p, q, thence s and the bounds for your confidence interval.