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From my memories of statistics class:

the way an actual statistician would try to answer this question would be to first describe a "null" hypothesis, called H0, then talk about the probability of seeing this set results, or an even more extreme set, if H0 were in fact the case.

H0: The police do not change their ticket collection strategies at the end of the month

H1: They try to collect more tickets at the end of the month than the other days of the month

H0 would describe some distribution for the numbers you are seeing. This is where you can put all of your assumptions about how things are - so that you ultimately end up with a model that generates a certain distribution.

Under this model, there's going to be a certain probability of seeing this result, or a more extreme result.

If that probability is less than, say, 5%, then this is saying that you'd only have a 5% chance of seeing these numbers given that there isn't in fact any conspiracy to collect more tickets.

In such a case, you might then "reject" the null hypothesis in favour of H1.

If the probability was higher than 5%, you might say that there is no "significant" evidence in favour of H1.



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