Thanks for the response.

I will try to explain my problem better. For example, I have three grocery stores, each month there is a number of complaints. We count the number of complaints monthly.

I have now 24 months of data, with on average 7 complaints (each month), standard deviation of 1,75.

I'm going to make a change in my store that I believe will lower the number of complaints by for example 50%. So if I'm using the z-test, my idea is to define the hypothesized population mean ("m" in the equation above) as 3,5 (50% of the current complaints mean value).

My Question Is: For how long will I need to run my experiment to have enough data to compare (to the old data) and get a satisfying results. (So you can say that I am trying to calculate how big the "sample size" needs to be.)

How can this be calculated with a confidence interval already defined.

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The way I estimated this at first was using the z-test, and solving "n".

n = (s^2*z^2)/(m-x)^2

where

z = z-score

x = sample mean

m = hypothesized population mean

s = population deviation

n = sample size

BUT I THINK THIS IS NOT CORRECT, ANY SUGGESTIONS HOW THIS CAN BE DONE? Thanks