MTH 380 Lecture Notes - Lecture 8: Vtt Technical Research Centre Of Finland
9 views8 pages
V {f-{1,CtJ/1Le
ideanu tv /*+,Wo'L, An
[rta, lO.ft 8r p.trtl
--
(1lA random sample bf n = l-5 observations was selected from a normal population. The sample mean and
variance were x :3.91 and s2 =0.32l4.Find a90% confidence intervalforthe population varianceo2.
(t+t M$h,^,,ffu^AL th/Wdt f,1" ftu YoPrilr,Aor^ vdttdr^'l is
X'qr,nn t'r-q, n,
T'r.orrlq ' z3.58a , T'o.gsr rq : g,t+d !
900/o *p-Aa'ut vr|'+,.l.tat },r {'hs PW
Tt0.of,rv ? zo,!$r tq
t\ (0.32t,{l }e L < J!fg. larql
lF z3.6gt 6.t+t.
= o.os
VCIilA-U,'.t"1 lS
4=
2-
T'*,h-r
2 3 .685
{-J= C.g0'
rL
fu r-tr h-r
Tz.
o
(r-l\ tg*{" * ^&;doNL *,/+,rt
/
G,l) 52' ./
q
hhmngt-!_54,14^4{4 ffi
-f ar t,? *,lz- -^
Xt.oo 1 a
NL
€tt?;F 1.03+ l,otl. + oSqrT-[TgT
Ll.-r)(a
----
YL
rr .4 -!ru-t
t
I
ameters of the pieces are normally distributed.
valtta.+ut- d z.
XL,h-r
SL=
t-
) r'-
t_ 4t1 - '1 ,01 +
i=r
I
1d^/A
h
0 fo,qr1 s
.: &l
t=t = (1,0r)z o ta,s+ll t (t.o3Jz r,(,t.or) 2tto.33lz+ (o.qs), r.
+ &,g
S"=
i). *[,,r]. + [.of =
g,1 0 rt - 3=9s z'
fr5 = 0,000 6OL+g = @
* so.oot'l 1-b = o,$st'
\t o.gssrB = l,)\-
.9, 10 sI
I-& = 0r,gB ;
Tto.o.v, I = 2l
Ji s 0,.0(
,96
39n/o twhV,ry i'l./+w*L A
044 pOtrw,larhulL vamrtatv<!_ .
'tt _
E LCI,ooo6) .t 6, t
e[. 9.6 ,4\
0lq4 a
h* 4
I
I
Finda90%confidenceintervalforpopulationvariance.Assumethatasampleof obtainedmeasurements ssee.:el
from normal population of all possible measure that can be obtained for the given object.
<6t(
zb,,-,
h = q.
h
Eut (Zx; JL
r=t h
h_l
= 3S3+ 3st +3s(+isS s ll'ttg
= 3s3z + 35-lL+ 3stt + Ssst =
3
4-*.: 0r50.-' f*= 0.,10 -+
Wd-t 1ilr- wfu,nrotl" 'gh 5z'
Ih*r)Sz
az
{r, 1-t r }r-r
St =
\
Zu
i:t
E*t'
l:r
r7-
3 = 1.8,1 5X'u, s r,3 :
0,0s I l-t s0.Xt
0,3te
=@
3.
&
Z
::]l r@
e}\
\-/
L
0.otl
9006
44 44
+"9[5 0; a,rt Se(Yr-t)'= ll,
/rl L-
Af precision instrument is guaranteed to read accurateiy to within 2 units. A sample of four instrun ent :ea: -:s c-
the same object yielded the measurements 353, 351, 351, and 355.
4,Yo'g <62< 3l.4zS.