Test a null hypothesis H0 : ? = ?0 and an alternative hypothesis H1 : ? ? ?0 , w

Question

Test a null hypothesis H0 : ? = ?0 and an alternative hypothesis H1 : ? ? ?0 , with ?0 = [1, -1] for bivariate normal distribution N2( ? , ? ). Evaluate T 2 and show that the Hotelling?s T 2 test rejects the null hypothesis at the level of significance ? = 0.05 . Suppose that the sample size is 30, the sample mean x' = [ 0.5, 0.5 ], and the sample covariance matrix ? ? ? ? ? ? 2 7 4 2 .

Test a null hypothesis H0 : ½ = ½0 and an alternative hypothesis H1 : ½ ? ½0 , with ½0 = [1, -1] for bivariate normal distribution N2( ½ , ? ). Evaluate T 2 and show that the Hotelling½s T 2 test rejects the null hypothesis at the level of significance ? = 0.05 . Suppose that the sample size is 30, the sample mean x' = [ 0.5, 0.5 ], and the sample covariance matrix ? ? ? ? ? ? 2 7 4 2 .

Explanation / Answer

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