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I sell a given product through 1000 shops & average revenue for that product is 2400 dollars per week per shop, with a standard deviation of 3100 dollars. I want to analyze, the offer ' three for the price of two' would be effective on my revenue or not, if it's introduced in 50 shops.

I understand that I should take average of 50 shops. But after that, I am not sure. How to go about it? .

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  • $\begingroup$ A linear model would be appropriate, where you would compare your regular product with your three for one "product" to check if there is a significant difference. $\endgroup$ – user2974951 Oct 4 '18 at 10:57
  • $\begingroup$ @user2974951 But shouldn't there be data for the three for one scheme, to do any kind of linear regression? $\endgroup$ – GeneX Oct 4 '18 at 13:06
  • $\begingroup$ Well yes, that was assumed. OP should collect data on these 50 shops for the three for one product and then perform the analysis. I don't see how he could do this without data? $\endgroup$ – user2974951 Oct 4 '18 at 13:11
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This is a matched problem hypothesis testing scenario(comparing revenue of shop before and after the scheme, henced matched problem). You cannot predict that if the scheme will effective unless you have the data of the scheme. You need to collect the revenue for the 50 shops before and after the scheme is applied. Then make inference if the scheme was actually useful. Get the data points then take the difference of revenue for each shop "i",

$$d_i = a_{i} - b_{i}$$ $$a_{i} \textrm{----> revenue of shop "i", after scheme}$$ $$b_{i} \textrm{----> revenue of shop "i", before scheme}$$

$$\textrm{Now you have 50 data points --> } d_{i}$$

You can get the mean, standard deviation of these 50 data points and do the standard two-tail hypothesis testing on the mean(t-test), with the null hypothesis as $$d_i = 0$$.

You can look up on google on how to perform hypothesis testing with t-distribution, or have a look here.

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