Transcription of Null hypothesis vs. alternative hypothesis
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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).
• A hypothesis is called simple if it completely specify the probability distribution and otherwise com-posite. Example 1 Suppose that we observe data y =(y1,···,yn). If we are willing to assume that the data set is a random sample from N (θ,10) where θ ∈{1,2}. We want to check which value of θ is consistent with data.
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