N
Newcomer101
Member
I am having difficulty deriving the pivotal quantity for the above confidence interval. (pg 24 chapter 11)
Taking two random samples:
A~bin(n1,p1) approximates to N(n1p1,n1p1q1)
B~bin(n2,p2) approximates to N(n2p2,n2p2q2)
Then A-B approximates to N(n1p1-n2p2,n1p1q1+n2p2q2)
Therefore, should it not follow the pivotal quantity should be:
(n1p1-n2p2)-(theta1-theta2)
sqrt(n1p1q1+n2p2q2)
Any help most appreciated.
Taking two random samples:
A~bin(n1,p1) approximates to N(n1p1,n1p1q1)
B~bin(n2,p2) approximates to N(n2p2,n2p2q2)
Then A-B approximates to N(n1p1-n2p2,n1p1q1+n2p2q2)
Therefore, should it not follow the pivotal quantity should be:
(n1p1-n2p2)-(theta1-theta2)
sqrt(n1p1q1+n2p2q2)
Any help most appreciated.