Suppose Π1 and Π2 be two populations of plants of two distinct varieties of wheat. The...

Suppose Π1 and Π2 be two populations of plants of two distinct varieties of wheat. The measurements of each member of these two populations are x1 = plant height x2 = length of ear.
Assuming that these observations were sampled from two-dimensional normal populations with unknown mean vectors µ1 and µ2, and the same covariance matrix Σ. The sample mean vectors and pooled covariance matrix of observations from Π1 and Π2 are: Use the Hotelling two-sample Τ2 statistic to Test for a difference in the population mean vectors. (multivariate analysis)

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