Thread: What goes wrong?

are independent IID samples from two normal populations sharing same variance

I can't show that the distribution of

What I did was to make use of the definition:

My Z is

but I can't continue after this

Hello,

But Z has to be a normal distribution N(0,1)

Assuming Y1 and Y2 are iid samples of N(0,1), then we have :
- Y1-Y2 follows a normal distribution (because they're independent)
- E(Y1-Y2)=0
- Var(Y1-Y2)=n1+n2

So in order to get a standard normal distribution from Y1-Y2, find a such that a(Y1-Y2) follows N(0,1)

And for that, recall that if M~N(m,s²), then aM~N(am,a²s²)

Can you try to do it ?

Also, please post all the information you're given, because I feel like there's not everything here

Hi, this is actually not a question but I'm trying to find out the derivation: The notes go like this:

(Two Normal Populations with Equal Variance)

Let and be independent IID samples from two populations with means .

Under the null hypothesis

then the distribution

So I suppose my Z is standardised already? since and ?