CT6 Q&A Bank 3.30 (iii)

Hi there,
Could someone please flesh out the solution to this. I don't get why we go back to using the individual sample variances instead of the pooled sample variance in the answer. And not sure where the root 2/n comes from.

Thanks,
Tom

 

See the pic attached below. And root 2/n has come from (1/n1+1/n2)½ = (2/n)½ Since n1=n2 here.

 

Thanks very much Bharti