Reasoning behind the inference conditions

What are the reasons for using the different inference conditions? Like the 10% condition, random condition, Normal condition, etc

The 10% condition allows us to assume that when making random selections, one selection is just as likely as any other every time (i.e. the selections are independent). The large counts condition and central limit theorem allow us to assume that the sampling distribution is approximately normal, regardless of the population distribution. It is also important that random selection/assignment is implemented, as random selection/assignment give us unbiased data from the population of interest. Hope this helps!

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