Actuarial Outpost CAS3 spring 2005 : Q# 23
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

Meet Valorie Mulder, DW Simpson Senior Recruiter

 CAS 3 - specific material Please keep posts regarding material common to both exams in the upper forum

#1
04-24-2007, 11:38 AM
 piemedia Member Join Date: Oct 2006 Posts: 61
CAS3 spring 2005 : Q# 23

Why critical region is X<= C, but not X>= C , because for type I error, the significance level is 2%. Isn't it x>=c for the significance level???
#2
04-24-2007, 12:04 PM
 YuGoHUGO Member Join Date: Sep 2003 Location: USS Enterprise Posts: 75

the critical region IS X>c, where c=30 accidents... they want to make sure that 98% of the sample falls below this 30 accident mark
#3
04-24-2007, 12:10 PM
 piemedia Member Join Date: Oct 2006 Posts: 61

oh,,,,,,, i see,, thank you so much,, good luck on your exam!!!
#4
04-24-2007, 12:28 PM
 carrytheCrøss Member CAS Join Date: May 2005 Posts: 2,769

Preface: YugoHugo beat me, but here's the post anyway =0

piemedia, the definition of a Type I Error is P(Reject H0|H0 is true). The null hypothesis in this question is that the proportion of customers who file at least one claim, p, equals 30% (p=30%). Since a discount will be offered if fewer than 30% file at least one claim, the alternative hypothesis is that p is less than 30%.

Now just work from the definition, and note that the proportion X who file at least one claim has mean p and variance p(1-p). And, remember that the $Var(\overline{X})=\frac{Var(X)}{n}$

$P(\text{Type I Error}) = P[\overline{X}.

The rest, I hope, should follow.
__________________
a wonderful post

Last edited by carrytheCrøss; 04-24-2007 at 04:47 PM.. Reason: Meant 'proportion'

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off

All times are GMT -4. The time now is 07:34 AM.

 -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top