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Chapter 8 - CHAPTERS Jn Jii 8-1 a Theocmfi denoe lew:l tor...

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CHAPTERS 8-1 a) Th eocm fi denoe l ew: l tor X- 2.1 4u I Jii < f1- < X + 2.1 4c I Jn i sd etennined hy tlt e \ 'a lt> eof'1-o which is ::! .14. From Table lll. ¢( ::! . 14) = ffL <2 . 14) = 0.9838 and theoon fi denc:e lt\ 'tl is .2 (0. 9838- o.s) = 96 . 76% . b) Tlt .eoon fi denc:e lt\ 't l fo r X - 2. 49a I Jii < 11 < X + 2.49a I Jii i sd ctermi ned bytf!.e byt.ft.eva ln.cott.o which is 2. 14 . From Table lll.<ll(:L49) = P("L < 24 9) = 0.99.)6andtheoo nfi deooe l e".'ti i s.:l{0 . 99~ S) = 98 . 7.2% . c) TJ! .eoontidmce l t'.>e l tbr X -l. SSo- / .Jii < Jl. · <X+ l. SSu I ..[ii i s<k."'ermined bytlt(: bytf!.eva ! t>eof'l.(). wl\ichis ::! . 14 . From Table lll. ¢(1.8 .5) = ffL< 1.85) = o . 9(>78andtheoonfid~ l a't l is 93 ..;6 %. 8•3 a) A 1.a = 1.29wocldgjve res-ul t ina 9Q%one-s i <k:d co nfi dence intm'<ll . b) A 1<J = 1.6.; wouldgh\:' result in a 9s5;';one-sidedoonfidcooe: int cn:a l. c) A 1-(l = ::!.xt wouldg i ~ result i na <)95Wione-s id00oo nfi d.enoe inten'al. 8-5 a) S:lm p! emea nfr om tltet'irst oon fi denoe inter\'al = 38.0 ::! •{6l .()8-38.M)/.:l = .s o Sam pl e mean fr om tl:'f: seoondoonfidenci!int erva J = 39.9.5 4-{60 .o.s- 39 . 9.S)/::! =s o b) Th e9.:;%C l is ('\B.M. 61 .98)aod tf! .e QO%C l is ('\9.9.;. M .o .:;) . Tlt.e high.o."f' tf! .eoontidmce lt\'t l. tf!.e\,ider th eC l. 8-7 a) Findnf or tf! .e l eng t boftJ!.ey.:;WiCl tobe40 .7 "8 / 2 = 1.¢ > / 2 l eng th = (>. <)6X20)/ .[ri = 20 392= 20.fri n = ( 3 ~~ 2 t = 3.84 Tt.ercl' ore. n = 4. b) Fi nd n for tf!.e l e~th o ftf!.e '!)!)~C l to be40. 7"' /2 = 2.:;8 1/ 2 length. = {t. <)6X20)/ ..Jn = 20 39' = 20.fri n = ( 5~06 r = 6.66 n .e refore. n = 7. 8-9 a) The 99W.Cl on tt.cmeanea lcit!m oonce ntratio nw o cl d be longer. b) No. th.'t t is oot tf! .eoorrcct interpretation of a oo nfidenoe int moa l. The probability thst .11 is between 049and0.82 i scitJ!.e ro or 1. c) \' es . this is theoorrect ioterpr i!'ta ti onof a oo nfideooe: int erva l. Tlteuppcr and l ower limi tsoft~.eoonfid.enoe limits are Nndom \'ariab! cs . 8- 11 95%Two -si ded:C l on t~ .etruemeanyie l d: where. ?= 90 480, 0 = 3 . n = 5 and"Lo .O :l,5 = 1.¢ . X - z 0 . <Yb -u I ../n < 11 · < X + z 0 . 025 o I .{ri 90 .4 80 - 1 96 (3)1 .[5 < 11 ·< 90 .4 80 + 196(3) 1.[5 87 . 85 < ,u < 93 .11 8- 13 a) '!)9%'[\.\.·o-s idedCI on tr..e trn.e mean piston ring, diameter fOr a= O.Ol,7.a,f::!. = 1-o . oo.; = 2,s8 .and .Y = 7 4. 03"6. o = 0.001. n = 1.5 x - z o.oos( ~ ) < 11 < x + zo o os ( Jn ) 74.036- 2.58( 0 · 001 ) < < 74.036 ° 2.58( 0 · 001 ] .Jf5 - 11 - T .Jf5 74. 0353 5, 115,7 4. 0367 b) '!)9% 0ne-si d.edC t o oth.etn~m ea npist o nring diameter fOr a= O.OJ.ZQ = 1.o .o 1 = ~,3.3 and .'i = 74 .0:}6. o = 0.001. n = 15 - 0 < X - Zo. O J .{ri - 11 7 4. 036 - 2.33( 0 ~ 1 ) < 11 74. 03545,11 Tlte l owe r boundoftheone -si ctedoonficteoce intm'al is l ess tf!.an tr .e lo,,•er hound of t lte tw o-si ded oo ofi deoce . This is because the 'f) opel pro b.!lbility of 9¢\Sonesided oon fi deooe intm'SI {o r a= o. Ol ) in t he l eft ta il to r int~ .e loh·er bound) is greater than Type [ probabilit yof 99% f\.\. ·o-s i d:i:doo nfidenoe int erva l (o r af !! = o.oo.s) int.f!..e left tail. 8- 15 a) 95~ t wo-sidedCI o~ th e mean oom p resshutrength f.a/2 = 1.0 .0 ::!.,5 = 1. ¢.aod .f = .)-2.;0,o = 1000. n = 12 x - Zo ms ( ~ ) < 11 < x + Zo o2s[ ~ ) 3250 - 196( 31 62 ] < < 3250+ 196( 31 62 ] Jfi - 11 - Jfi 3232 .11 < 11 < 3267. 89 b) 9!)%Two-sidedCl on the true mean oom pressh 't strf:Dgth f.a/2 = w. oo.s = 2,:;8 x - Zooos( ~ ) < 11 < x + Zooo s( Jn ) 325 0 - 2 .58 ( 3 ~~_2) < 11 -< 3250+ 2.58[ 3 ~ 2 ) 3226.4 < .u < 3273 .6
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8- 17 Set tlt.ewi dth t o6 ~ .o l! rs witho = :!:.),ZO.O:i,s = l. 9f>so h '£'fo r n.
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