Question

12. An actuary considers a portfolio of 40 policyhol ders which was t aken as a random sam ple from a block of business. She discovers that 11 of these policyhol ders were each compensat ed over $ 10,000 last year Construct a 94% confidence int erval for the proportion of policyhol der s who were com pen sated 10,000 or less last year from this block of business.

Answer 1

P9.2001 Solution: Given :- → patholio of 40 policyholders ► discovers !! policyholders Compensated over $10,000 last yeca → 94% Confidence interval » Compensated $10,000 → Sample proposition peap discovers whee, n=40 discovers = 11 - Ho a. plap 0:275 → Standard esesh | Se = sqrt (pcap & a peap)/n) ] where, peap = 0.275 , n=40 - Sart (0.275 * (1-0.375)) 40) s part (0.275 * 0.013125)

9.00 - 0.070600 St = 0.070GOO → Confedence Interval 94% -0.94 x=1-0.94 = 0. OG 3.X = D.OG → X/2 = 0.06% e 0.03 Zala = 1.88 [z value for confidence intercal] » Confidence interval I c = (pcap - 2*st, pcap & z e sf) whare, plap = 0.245 , Z=1.88 36 = 0.0706 0.275-1-88* 0.0706, 0.275 +1.88 * 0.0706) - (0.4492 , 0,6077) ... confidence antewat = 0.1489,0.4077