Significant difference between sample and population over time I am comparing the daily number of stock depletions between multiple stores to identify stores with a significantly high number of depletions. 
I'm thinking that the appropriate method is a one-sided Z-test in which n= number of days for which observations are available, X= mean number of depletions per day for a given store (sample), and μ= mean number of depletions per day for all other stores (population). 
I will perform this test for each store and correct for multiple testing by dividing p= 0.05 by the number of stores. 
Is this correct? Thanks in advance!     
 A: See questions in my comment. Assume every item is equally likely to go out of stock on any one day. Suppose Item A out of stock for three days counts the same as Items A, E, and Q out of stock on Tuesday.
For each store in the population count item-days in both numerator and denominator of a fraction. If a store had 1000 items and was open for 25 days last month, then it had 25,000 item-days. Then maybe the store had 1750 item-days of depletions. (That could be all 1000 items out of stock on one day
and 750 out of stock on another day, or it could be  70 items out of stock on all 25 days.) Then its outage percentage was $p = 0.07.$ 
Do the same computation collectively for all stores in the population. Get numerator and denominator for the whole population. Maybe you get $p = 0.0682$ for the population last month.
Maybe a particular store of interest had 23,000 item-days last month, and
$x = 1518$ item-days of depletions. Is that significantly less than in the population? Assume item-days are indpendent (very unlikely).
If this store were typical of the population last month, it should have had
$X \sim \mathsf{Binom}(n=2300, p=0.0682)$ item days of depletions. Then $P(X \le 1518)=0.094 > 0.05,$ so at the 5% significance level this particular store was not doing significantly better than the population last month.
pbinom(1518, 23000, .0682)
[1] 0.09455519

Whenever I see binomial models with such large $n$ and relatively small $p,$ I wonder if there is a slightly different formulation of
the situation, using a Poisson distribution, that would be simpler.
Does it matter if the store is out of an item on a day when nobody
wanted that item? Maybe what you should count is the number of sales
lost in a month due to depletions. Modeling that count as Poisson might work.
Maybe a more direct approach would be to get the total revenue lost per
month due to depletions, and try to model that.
I am not recommending my formulation above, just illustrating how many
questionable assumptions I had to make in order to get a tractable
model. 
