Statistical Test for a Poisson Distribution

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I've done an experiment where I have several stochastic data which probably comes from a Poisson distribution (according to my peers). I have to test this, but I'm not sure which test to use or exactly how, in my statistics class I've only seen the type of tests that are used for the mean or standard deviation. Please help!

Also, side question, if the data where to have a Poisson distribution, would it be the same to acquire data continuously and then separate it into several parts to do statistics and acquire data by measuring, stopping, and then measuring again?

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HINT

Do the Kolmogorov-Smirnov test.