Question

In t-distribution for two independent samples n1 = n2 = n, then the degrees of freedom is equal to:
2n–1
2n–2
2n+1
n–1

Answer 1

For a t distribution,

If A and B² are the mean and variance of a random sample of size n from a normal population with mean u and variance p²,then

$M=\frac{A-u}{\frac{B}{\sqrt{n_{1}}}}$

has t distribution with $n_{1}-1$ degrees of freedom.

Similarly, using the above formula for t-distribution we can say that sample $n_{2}$ has  $n_{2}-1$ degrees of freedom.

As, sample $n_{1}$ =n,has n-1 degrees of freedom.

And sample  $n_{2}$ =n,has n-1 degrees of freedom.

So, each sample has n-1 degrees of freedom by t-distribution.

Then, total number of degrees of freedom=n-1+n-1=2n-2

Or separately each sample has n-1 degrees of freedom.

Option (B) 2n-2