Let Y 1 Y 2 , , Y n1 , be a random sample of n 1 observations from a normal distribution with mean 1 and variance 1 2 Let X 1 , X 2 , , X n2 be a random sample of n 2 observations from a normal distribution with mean 2 and variance 2 2 Assuming the samples were independently selected, show that has...

We want to show that the statistic F F S12S22 2212 has an F distribution with v1 n1 1 numerator degr ...

Let Y 1 Y 2 , . . . , Y n1 , be a random sample

Question:

Let Y₁ Y₂, . . . , Y_n1, be a random sample of n₁ observations from a normal distribution with mean μ₁ and variance σ₁². Let X₁, X₂, . . . , X_n2 be a random sample of n₂ observations from a normal distribution with mean μ₂ and variance σ₂². Assuming the samples were independently selected, show that has an F distribution with v₁ = (n₁ - 1) numerator degrees of freedom and v₂ = (n₂ - 1) denominator degrees of freedom.