a) What is the difference between a 𝜒 2 -test of homogeneity and a 𝜒 2 -test of independence? b) When should you use a p

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a) What is the difference between a 𝜒 2 -test of homogeneity anda 𝜒 2 -test of independence?
b) When should you use a paired sample test for means?
c) Why do you need to check if each cell contains at least 5expected (or observed) counts when conducting a 𝜒 2 -test?
d) What theorem are we relying on in order to conduct parametrichypothesis tests? State the theorem’s name and the colloquialdefinition.