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Null hypothesis vs. alternative hypothesis

Econ 620 Null hypothesis vs. alternative hypothesisSuppose that we have datay=(y1, ,yn) and the data is generated by the true probability distributionP 0,from a family of probability distributionP indexed by .We can partition the parameter space into two subsets, 0and , consider the following two hypothesis ;H0; 0 0HA; 0 AH0is called thenull hypothesisandHAis called thealternative hypothesis . The union of null andalternative hypothesis defines a hypothesisH = 0 Acalled themaintained hypothesis . A hypothesis is called simple if it completely specify the probability distribution and otherwise 1 Suppose that we observe datay=(y1, ,yn).If we are willing to assume that the data set isa random sample fromN( ,10)where {1,2}.

Econ 620 Null hypothesis vs. alternative hypothesis Suppose that we have data y =(y1,···,yn) and the data is generated by the true probability distribution Pθ0, from a family of probability distribution Pθ indexed by θ ∈ Θ. We can partition the parameter space Θ into two subsets, Θ0 and ΘA. Now, consider the following two hypothesis;

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  Alternatives, Hypothesis, Alternative hypothesis

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