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Let X 1 , X 2 , . . . , X 13 and Y 1 , Y 2 , . . . , Y

Let X1, X2, . . . , X13 and Y1, Y2, . . . , Y16 represent two independent random samples from the respective normal distributions N(1, 1) and N(2, 2). It is given that 12= 1/5 22 , but 22 is unknown. Construct a ratio that follows the t distribution with 27 degrees of freedom.

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