Confidence Interval on proportions for 5 variables based on 5 samples? We distribute an ecological fertilizer for soils. A client of ours is asking for confidence interval on 5 key parameters.
We have run 5 samples of soils in 5 different places where our product has been used. 
The samples have been analysed and we now have the values for each of these 5 parameters from each of the samples:
Parameter 1
Sample 1: 0.058
Sample 2: 0.069
Sample 3: 0.041
Sample 4: 0.052
Sample 5: 0.062
Parameter 2
Sample 1: 0.078
Sample 2: 0.079
Sample 3: 0.061
Sample 4: 0.082
Sample 5: 0.072
etc... 
How do I calculate the confidence interval for these 5 parameters based on the 5 samples?
I am not sure about what my n (sample sizes) really are? 
Should each of the 5 samples be defined as sample size 1 (n=1)
Or are we talking sample size 5 (n=5) for each of the parameters?
Thank you so much!
 A: If the question is about the 5 different means within each of the 5 sets of parameters, then your sample size is 5, and that's what it sounds like you're doing. It sounds like your "parameters" are different locations, and each of your 5 samples in each location are essentially identical in how they're done, so the variance in their values is random. Since you can't take infinite soil samples in each of the 5 locations, you need to estimate the true mean value from a finite number of samples, in this case 5 for each. Don't let the word "sample" confuse you here - if you "sample" the soil 5 times in the same location and get one value of interest from each of these soil samples, then your overall sample in statistical terms, which you're using to estimate the mean value of a theoretically infinite number of soil samples, is 5.
You can do this by hand (or close to it) - the Wikipedia page on t-tests has the formulas, including the link to calculating standard deviations - but here at least is proof that it can be done here and that it makes statistical sense. The following code in R will give you your confidence interval for parameter 1:
t.test(c(0.058, 0.069, 0.041, 0.052, 0.062))

Which gives you this output:
One Sample t-test

data:  scores
t = 11.901, df = 4, p-value = 0.0002856
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 0.04324188 0.06955812
sample estimates:
mean of x 
   0.0564 

Change the five values in between the parentheses and you can get the confidence intervals for the other parameters. Your sample sizes are small, of course, but what's small and what's large always depends anyway on how complicated and chaotic is the phenomenon you're studying, and more importantly, the whole point of the statistics is to ensure that your confidence levels accurately account for the size of your sample relative to the variation you seem to be dealing with.
P.S.: Note that you can also certainly compute a confidence interval for the mean values regardless of parameter/location. Then your sample size is 25, and it might certainly reflect something meaningful since your soil samples evenly represent all five locations. Hopefully, if nothing else, this illustrates how your sample size and what counts toward it is very much a function of your research question and the statistic you're trying to estimate.
