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Null hypothesis vs. alternative hypothesis

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Econ 620Null 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 1Suppose that we observe datay=(y1, ,yn).If we are willing to assume that the data set isa random sample fromN( ,10)where {1,2}.We want to check which value of is consistent with , we can formulate the hypotheses;H0; =1HA; =2Here, both null and alternative hypotheses are simple since mean and variance are sufficient to completelyspecify a normal distribution.

Testing joint significance of slope coefficients in linear regression model is an example. 1. ... determine the plausibility of the null hypothesis. We need a kind of summary measure of the data, which should be handy but retain relevant information on the true data generating process.

  Testing, Summary, Alternatives, Hypothesis, Alternative hypothesis

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