Small population (<100) reliability for clusters - confidence interval and margin of error

We conducted an employee satisfaction survey among the employees of our 30 schools. There are 2000 employees and we had 1200 responses. I can calculate a margin of error with different confidence levels. But, my director wants me to calculate this for each school seperately. How can I calculate the margin of error for the results of a school with a population of 20 employees and when I have only 8 responses ? Or for the school with 80 employees and only 35 responses ? Or the school with 320 employees and 190 responses ?
Can I calculate this ? Should I tell him the population is too small ?
The questions were likert scale questions. My director would like to be able to say: “In that school 80+/- 10 percent of the employees are happy with … and I am 90 % sure of what I say”.
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Active Member
Hi Vandestra.

If all the employees would answer you wouldn't need a confidence interval this case, the answer will be one exact number.

Try looking for "confidence interval of a finite population" and use the correction
Since the sample is a big portion of the population the confidence interval will be more accurate than if you use an infinite population.

You can do a confidence interval for a small population under the assumption that the distribution is normal (using the t distribution)

8 from 20 is not too small ...