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Hypothesis testing for the common mean of two normal distributions in the presence of an indifference zone

  • Steven W. Klein
Article

Summary

LetX1,...,Xm andYt,...,Y be independent, random samples from populations which are N(θ,σ x 2 ) and N(θ,σ y 2 ), respectively, with all parameters unknown. In testingH0:θ=0 againstH1:θ≠0, thet-test based upon either sample is known to be admissible in the two-sample setting. If, however, one testsH0 againstH1:|θ|≧ε>0, with ε arbitrary, our main results show: (i) the construction of a test which is better than the particulart-test chosen, (ii) eacht-test is admissible under the invariance principle with respect to the group of scale changes, and (iii) there does not exist a test which simultaneously is better than botht-tests.

AMS 1970 subject classifications

Primary 62F05 Secondary 62A06 62C15 

Key words and phrases

Common mean indifference zone t-test invariance 

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References

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Copyright information

© The Institute of Statistical Mathematics, Tokyo 1982

Authors and Affiliations

  • Steven W. Klein
    • 1
  1. 1.Rutgers UniversityUSA

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