How do I pick a rule for decision of a bilateral test?












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I have a two random samples normally distribution of length $m = 10$ and $n = 12$. Everything independent.



I need to find a rule of decision of level 95% for the hypothesis of equality of the two random variables.



Now, I know about this confidence interval useful when studying the $frac{sigma_Y^2}{sigma_X^2}$:



$$ [F_{1-frac{alpha}{2}}(m-1,n-1)frac{S_Y^2}{S_X^2},F_{frac{alpha}{2}}(m-1,n-1)frac{S_Y^2}{S_X^2}]$$



My problem is that this is not bilateral and I do not know how to answer the question: "finding the rule of decision of level 95%"










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    0












    $begingroup$


    I have a two random samples normally distribution of length $m = 10$ and $n = 12$. Everything independent.



    I need to find a rule of decision of level 95% for the hypothesis of equality of the two random variables.



    Now, I know about this confidence interval useful when studying the $frac{sigma_Y^2}{sigma_X^2}$:



    $$ [F_{1-frac{alpha}{2}}(m-1,n-1)frac{S_Y^2}{S_X^2},F_{frac{alpha}{2}}(m-1,n-1)frac{S_Y^2}{S_X^2}]$$



    My problem is that this is not bilateral and I do not know how to answer the question: "finding the rule of decision of level 95%"










    share|cite|improve this question









    $endgroup$















      0












      0








      0





      $begingroup$


      I have a two random samples normally distribution of length $m = 10$ and $n = 12$. Everything independent.



      I need to find a rule of decision of level 95% for the hypothesis of equality of the two random variables.



      Now, I know about this confidence interval useful when studying the $frac{sigma_Y^2}{sigma_X^2}$:



      $$ [F_{1-frac{alpha}{2}}(m-1,n-1)frac{S_Y^2}{S_X^2},F_{frac{alpha}{2}}(m-1,n-1)frac{S_Y^2}{S_X^2}]$$



      My problem is that this is not bilateral and I do not know how to answer the question: "finding the rule of decision of level 95%"










      share|cite|improve this question









      $endgroup$




      I have a two random samples normally distribution of length $m = 10$ and $n = 12$. Everything independent.



      I need to find a rule of decision of level 95% for the hypothesis of equality of the two random variables.



      Now, I know about this confidence interval useful when studying the $frac{sigma_Y^2}{sigma_X^2}$:



      $$ [F_{1-frac{alpha}{2}}(m-1,n-1)frac{S_Y^2}{S_X^2},F_{frac{alpha}{2}}(m-1,n-1)frac{S_Y^2}{S_X^2}]$$



      My problem is that this is not bilateral and I do not know how to answer the question: "finding the rule of decision of level 95%"







      statistics hypothesis-testing confidence-interval






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      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Jan 25 at 16:45









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