Question

Assume that a sample is used to estimate a population proportion p. Find the 95% confidence interval for a sample of size 169 with 128 successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places. C.I.

Answer 1

Þ. Solution - Here b. is the populaition parameter of success. We draw draw X,X2, X169 samples from the population parameters unkno known) to estimate Nr. C I (95%) Xi = 1 ith sample gives success Otherwise Xinbera (pl. ; 1=1,2 - 1169 of ºp? qi 식 169 ZXiN i ㅋ PUA xil is شاندار کا Bin (169, b) ; E(2x)=1696 denotes no. of successes in 169 samples drawn. i since sample size is large define T = Exi 169 NCO, 1) VIGO (1-P) [CLT Thesnen We do not know þ. Voer(EX) = 1696 (1-6) has to be since sample size is large, van (IX.) p Cl- CI-P rarcaxi) i 3 169 Known. P Where = 169 169 ZX

IA then & Neo) 95 100 169 T, 2x; -1695 √ 169 p*(1-A P ( -20.025 5 1 <20.025 MP [-20.025 < -169< 20.025 11695" C1-P) 키 p[-70.25 169 (1-1)+1699 2x< 20:0251 PCI-F) 169 8 95/100 7 p[XX-ligG/160$ (1-6) < 1&9B < %;+1.962169$ (1-1) E 95/100 + 16ap 164 = 0.015 .: 95%..confidence interval of þ 169 is Exi i si 1.96 / 169" (+2) 169 T69 Ixit 1.96 5169$CLP) te Estimate of pro 128 31469 .. et non confidence interval stimate of 'p is tba -1.91769 HUF is

Obseve ved values. -Criven 169 EX Vem 128 is 169 Þ^ = /28/169 ::: 95% confidence interval estimate of 128-46 164 x 128/169*(1-128/164) · 188+1.96 XS169 x 128/169X/1 – 128/169) [0.6927 008220244 [0.693, 0.822] 169 ११ ANS met