Point me in the right direction for a confidence interval

#1
I am working on a project now where we sampled 200 locations to gather information. The enterprise has over 700 total locations. Using the information I gathered I calculated the average ratio of PC's to paid employees in each location. I then used this ratio to forecast the number of PCs in the un-sampled locations (I know the number of paid employees in each location). I would like to publish some confidence interval to these numbers. Most important, to the total number of PCs I forecasted and not the numbers I came up with for each individual location.

I went to school as an Industrial Engineer 25 years ago and took lots of stats, so I'm somewhat familiar but very rusty. Could someone point me in the right direction to what methods I should be looking up to do this?

If you need details let me know.
 

mp83

TS Contributor
#2
(Ignoring the sample design...)

You can get an estimate by the weighted-size mean

m=Sum{n(i)*m(i)}​

and variance

var=Sum{n(i)*s(i)^2}/{Sum(n(i))}^2​

You can use that to get an asymprotic C.I, as a Central Limit Theorem assures us that weighted means converge to a Normal Distribution.
 
#3
you can use your ratio as a continuous variable. Calculate mean ratio and its standard deviation. Then you can use the formula to get the confidence interval. I have a glossary on my webpage that lists the formula and the tables. You can also use linear regression (provided that your values are not skewed). With it, you can estimate the number of PCs for different number of paid employees. If your values are skewed, you will need to transform the variable first.

Jenny Kotlerman
www.statisticalconsultingnetwork.com