Question

Using the plug-in method determine A >0 such p (1-p) (1- A),p (1-p)(1+ A)] is a confidence interval for p (1 -p) with asymptotic level 95%. Note that A should only depend on n and p (Enter hatp for p. If applicable, enter Phi(z) for the cdf (z) of a normal variable Z, q(alpha) for the quantile qa for any numerical value a Recall the convention in this course that P (Z< qa) =1-a for Z~ N (0,1).)

Answer 1

Answea Using the plug in method Azo Such Canfidenre inteaval fa ) a aith aymtotic level 95% Hene A shoud only depend h and Noc t find the A - - let P-P) above ezuationi Noc diffenentiete the g'ir) 1-2P Z~No) neralk the Nos 3T is Fiven^j N ((9() Thanefe 3T)N/Ce-2) fa-) Comfidence asymp totic Noa Ce find inteaval f 3() Tiatis Pi-f) 95/ heed to Noc p (-2f (1-20 Y1-f)P 3T-a (e)<Td3-2P-V9/t)=1d modifies to beloc fm Noc the above eguation

(- d8-1)}| 0-1 then Ge get the belaw Noc by using the plug- in estima til? - T - 2f n. tere 1- Condence inteval Too So-D ol = 8/20 Thenefe the q5% Confidence intevel i give j 95C Vale given by Thesefae th nezuined A A 1-2p A