For i 1, ,s and j 1, , ni , let Xi,j be independent, with Xi,j having distribution Fi , where Fi is an arbitrary distribution with mean i and finite common variance 2 Consider testing 1 s based on the test statistic (13 29), which is UMPI under normality Show the test remains robust with respect to...

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For i = 1,...,s and j = 1,..., ni , let Xi,j be independent, with Xi,j having

Question:

For i = 1,...,s and j = 1,..., ni , let Xi,j be independent, with Xi,j having distribution Fi , where Fi is an arbitrary distribution with mean μi and finite common variance σ2. Consider testing μ1 =···= μs based on the test statistic

(13.29), which is UMPI under normality. Show the test remains robust with respect to the rejection probability under H0 even if the Fi differ and are not normal.

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