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

Salution proportional allocatin tor 34 40 284 x 44 284 40 6-197 hE 2 40 284 x 168 D 28 66 24 21

Page No Date foT has n3/40 56 284 E7.887 2.& for be 4 x16 4 284 2. 25 2 INumber of Seats 6 A4 91-40 41-50 24 168 1-70 2 6 71-0 N=284 D: 40 b) Here 17-1818. 20.1369 27.6892 38.5625 Population total 6300 998 1

Page No. Dato for A hl hel ks 882 1 (67 Mna NaT MMNarlye) 24990-4ex 882 21442 confidence interval varan) e (N .)= YM Yest ) Eh2 Var Nn n(N-n) 11 N- 2 NYN 288

154673- 264x 283 4875 10g15 289 52.5622 nN-0 Nar 2 Myi 1 (n-1 1 24970-40 5-1 24940-19448 39 141-58ヌ2 (N-n) (141-5870 2) =40(284-40 (141-S872 284 4&65-8136 95.10 Confidenee interval is Vor 745.27944, 1018.7205 Plalls ucho

Page No Date The methode used in sampling Sampling parte bee staatified is more effiefeot than Simple Random 1 13ecauce (F)sar( Nar