Let (x₁, y₁), (x₂, y₂), ..., (xₙ, yₙ) be a random sample of size n from the bivariate normal population. Derive the test statistic for testing the hypothesis H₀: ℓ =0 against H₁: ℓ ≠0 , where ℓ is the correlation coefficient between X and Y.
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