Let X 1 , X 2 , , X 13 and Y 1 , Y 2 , , Y 16 represent two independent random samples from the respective normal distributions N( 1 , 1 ) and N( 2 , 2 ) It is given that 1 2 1 5 2 2 , but 2 2 is unknown Construct a ratio that follows the t distribution with 27 degrees of freedom

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Question: 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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