Question

3. To estimate the total of the number of socio-democratic seats (SDS), y in a municipal council, the population was stratified into four strata using the total number seats in the municipal council. Some information about these strata is given in the following table. Population Sample Number of N NA 7 2 seats k-l k=l kl 1,647 9,735 8,294 5,294 756 31 -40 44 13,784 72,223 44,529 24,137 89 3,383 441 41 -50 168 51 -70 56 1,545 250 71 -... 16 617 102 a. Allocate a total sample of size, n 40 using the proportional allocation b. Estimate the total of socio-democratic seats for a stratified random sampling of selecting a sample of size, n = 40. confidence interval for the total. c. Estimate the total of socio-democratic seats if a simple random sampling scheme was used to select a sample of size, n = 40. Construct a 95% interval for the total d. Which of the two methods used in (b) and (c) is more efficient? Why? Construct a 95% W!

Answer 1

Solution a ttal Samle of Size , n= tfo using the foaop?itio- Ca) To alecate - Yel alloration there N we Knoa that ML then X168 (0.1408) xi6s 3. 654 then X4 6.1952 then 40 91 X 284 O.i408 x16 22538

fh3 then 56 3드 284 70.1408 X56 7.88 48 n-나0 tstaf 95 ontidencemteaval f the To Constuct that ... We kmow yK NL NA then ar et Nocs tSubstitute the 9iven Values K KEI 156 나4 -17.18 Nh Noc Nk s45 56 k 3383 68 26.137 NOw K삐 NL

Noc PaPulation total 14 6 300 Vay Vaon tel Var K Noa Vay 4 24A 358 Vany 2142 hyn 88 Var Now the 95- Confidence înteval cteae E ( Yl (N) Nocu Va N E 9 ()

Nn VaY Noc to find 5Value. EKno that (-5) 2 -h8B 15 4673- 28 4 Yw 8 SC 52.5622 Noc to fine Va A Var { tol - (-Nu ahesie (4-5) t h40 then 5. ) 9 .- 403 39 s9448 39 S59 39 141.587

Ves (y No tfinal te We knoc that (N-n) then Cre get ,s2Values in eruation Now toSubstitulr N, m Var (4.581) x4.587 09LL 38i8 8.2 Los.598t 5 Confidence inteval is giveaj No co the fmuia af 3 아teae d =Confidence inte val foo 0.05 Zo.05 -Zo ,025

fnom eguation A5-CI /2Var 11 9 b1 88 485-807 V (e1-755) 6-1 88 882t 36.7118 862-36.71f/ 8F2+ 136.71 98) 145.280 to i 8-720 Satisficd Samplin (a) used in (b) and (c) tene the method Sampling andom Samele Sihee mar efficient than Var <Va