The estimation of the regression coefficient of a population, defined by E Cv) ---3' + Ox, incorporating two preliminary tests of significance has been discussed. The experimenter has two random samples of different sizes from two such populations, as defined above, with regression coefficients 131 and 02 respectively, where /32 may possibly be equal to ~31. Besides this, it is also conjectured that the common conditional variance o: of the two populations has a specified value a~. The two preliminary tests are used to resolve these two uncertainties.
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