Calculating Confidence Intervals for survey results


I have what is probably a fairly basic question!

I am conducting a number of surveys looking at expenditure behaviour of audiences at an event. I want to calculate confidence intervals around the figures I have got for average expenditure.

e.g. For one survey, my total population is 66
There were 28 respondents
On average, the respondents spent £100 each at the event

What I want to know is what is the confidence interval on that £100, given that the figure is based on a less than 50% sample of the population?

I have found a formula for this, in this link

But this doesn't seem to take account of the size of the population. If I put in 28 into the "sample size" box, and fill in the other stats they ask for, it gives me a certain confidence interval, but what if my population was also 28? Then there would be no sampling error. I don't see how this formula takes account of this.

Also, I have found this
However, this works on percentages and you have to input a notional % result for a question with a yes/no answer (e.g. 50% gives the highest confidence interval). This doesn't seem relevant to what I need.

There must be some way of working out confidence intervals given the mean, standard deviation, the achieved sample and the population??

Can anyone help a stats-poor guy?



TS Contributor
The calculators you found use the exact same mathematical background that those in the last page, but what you see in the last website is the same formula with an additional term called finite population correction. If you have a very large population (like most surveys do) the difference is meaningless. Since you have a very small population, the correction is necessary. Just remember that those formulas are useful only if you used a simple random sampling, if you use strata or clusters, adjustments must be made.