Commenting on wider population from survey sample


New Member
I am conducting a survey in 9 restaurants, hoping to gather data on our customer demographic profile.

The population is equal to the number of covers the restaurant had over the corresponding period in the previous year. This ranges from 4000 to 10000.
Across all sites then, I understand that I would need between about 350 and 370 responses to collect data in the 95% +/- 5% confidence interval and margin of error.

I also need to apply a separate quota to reflect the number of covers that each site contributes to the total. Whilst the site with the fewest covers contributes 7% to the total, the busiest site contributes 17%.

The minimum total number of responses required then was 350/7%. I then calculated the quota per site from this number.
However, most sites won't fill this quota - the busiest site won't reach the 800 or so required responses, whilst some will far exceed their quota.

My question is, as long as the site reaches its minimum quota required for the 95% +/- 5% statistical confidence, can I then effectively 'scale' the results for that site up so that it matches its relative cover-weighted quota? Is this the same as extrapolation, which I understand is best avoided?

The issue is that, despite the fact that our restaurants are all the same brand, and all located in the same city, the customer base is very heterogeneous and demographic profiles vary hugely from site to site.

Apologies if some information is lacking, or the question is framed incorrectly. I have only a very rudimentary understanding of statistics and the administration and analysis of the survey has thrown up more questions than I'd originally anticipated.

Many thanks!