Let Y 1 and Y 2 be the means of independent random samples of sizes n1 and n2 selected from normally distributed populations with parameters ( 1 , 2 ) and ( 2 , 2 ), respectively If show that has a Students T distribution with v (n 1 n 2 2) degrees of freedom (n 1)S (n, 1)S n1 n2 2...

To show that the random variable T has a Students tdistribution with v n1 n2 2 degrees of freedom we need to demonstrate that T follows the tdistributions probability density function pdf First lets c ...

Let Y 1 and Y 2 be the means of independent random samples of sizes n1 and

Question:

Let Y̅₁ and Y̅₂ be the means of independent random samples of sizes n1 and n2 selected from normally distributed populations with parameters (μ₁, σ²) and (μ₂, σ²), respectively. If