Question 5 Suppose we have the following two samples: Sample 1: 711,...,n from N(#, 1), Sample...

 

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Question 5 Suppose we have the following two samples: Sample 1: 711,...,₁n₁ from N₂(#₁, Σ1), Sample 2: 21,..., 2n₂ from N₂(μ2, Σ2). Two new samples are defined through the linear transformations ytj = Caj + d for all l = 1,2 and j = 1,2,..., n, where C is a px p nonsingular matrix and d'is a p× 1 vector. Based on Samples 1 and 2, the T²-statistic for testing ₁ = 2 is denoted as T2. On the other hand, based on the two samples ₁1,1n₁ and 21,..2n2, the T²-statistic for testing the equality of vector means is denoted as T2. Show that T2 = ². Question 5 Suppose we have the following two samples: Sample 1: 711,...,₁n₁ from N₂(#₁, Σ1), Sample 2: 21,..., 2n₂ from N₂(μ2, Σ2). Two new samples are defined through the linear transformations ytj = Caj + d for all l = 1,2 and j = 1,2,..., n, where C is a px p nonsingular matrix and d'is a p× 1 vector. Based on Samples 1 and 2, the T²-statistic for testing ₁ = 2 is denoted as T2. On the other hand, based on the two samples ₁1,1n₁ and 21,..2n2, the T²-statistic for testing the equality of vector means is denoted as T2. Show that T2 = ².

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