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 (11 66), which is UMPI under normality Show the test remains robust with respect to th...

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

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 (11.66), 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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