B4090.HW5Solns - BTRY 4090 STSCI 4090 Spring 201 l Homework...

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Unformatted text preview: BTRY 4090 / STSCI 4090 Spring 201 l Homework 5 Solutions 1. Larsen & Marx p. 360, Question 6.2.1 modified. Z’L V‘v’lo W.sz ~ *5?“ = .3 : ~ {.61 AT. I”? Ho: fl=lZo (a) Ll): M$ [20 (Cl H,1/A<I HI: /A>!Z(3 20: ~ Red‘ece z*> z“)a 1,97 'icfiiffo Pflmme: P€Z > ‘l-él) T 0.9L/6Y>o.ojr&\jufl L‘F {:G:(fa Z Z > I‘LEH) : >01»? red'efiéf £15 P*W\(Ma == P(Z <—I.6i) = 0, 05‘35 <00? Reject: 0.0L! F—mime :: lZ-Cjficf 2X 4: .— Zaog = -[_ ,1“, V. SFQJec-E'l 2. Larsen & Marx p. 360, Question 6.2.2 modified. 04: O.l0 of. : 0.05“: w. =: O.(\{ D( : 0.0m; G‘rlf ya/L‘ n-1 2" ~ N(o I) ” 1 Wm ’ p ( I 57* Gig: \ >2 =Cfr‘ IS‘ - (c) >7< 35—- a if: (if) >7> qs~>+ Z H'- 4.421: ‘3’< 8311: Oh §>zoaze §<38 ?‘ Or 92>!01.2; 374 35.31:. or 3?;103.ZY 57¢ 89.98 on 37> 105:1 3. Larsen & Marx p. 360, Question 6.2.4. Be sure to state the model (specifying all assumptions), the null hypothesis, the alternative hypothesis, the test statistic, the critical region, the statistical inference, and the real-world conclusion. 6.2.4 Assuming there is no reason to suspect that the polymer would shorten a til-E’s iifetnne, the altemative hypothesis should be H}: #3 :> 32,500. At the a: [3.05 level, Ha should he rejected ifthe test statistic exceeds. 3.0; = 1.64. But 2 = EEOC—32,500 W. = 1.26, implying that. the. 40001.55 ObSEI'Ved mileage increase is not statistically significant. 4. Larsen & Marx p. 360, Question 6.2.6. 6.2.6 By definition, at: H299 31% 36.1 I Hg is true) = P M g m s’ M act/$15" 6.0!JE aomffé P(—0.07‘ S E S 0.0?) = Oflfifi. The filterval (29.93 38.1) is a poor choice for 0 because it rejects Hg for the j? — values that are most. compatible with Hg {that is, closest to ya = 33}. Since the aitemative is two—sided, H0 Should he rejected if j? is; either 1)£30 - LEW/gig» =21101‘ @230 + l.91~~§1EL =32.9. «.16 «fig S. Larsen & Marx p. 366, Question 6.3.4 modified. I _ nrzoo/ P:O_L(S‘ Large Sample fart“ X—b n _. Ee‘ecé F! P ~— X 6‘70 J _ mom—pt ?.03§€ > Zea 0!. r O. to : FeJecé if X> €413! d : 0.0:: red’eci: 04.: 0-01: bananas-E Reject. £16 SLACL‘ {Raf P(K3/ [is-20.51? 4 0< Mffnj mini-terse be CQ{CLA 2’an Comma/«Ema Probabili‘ffief 7Com BM (W,P3 Ni Befl‘é X:O-IO :9 Res: ’00 o<=o.os* => L851: (03 6&7. Larsen & Marx Question 6.4.4 modified: Construct and plot the power curves for the alternative hypotheses (a) Hl : ,u > 60, (b) HI : ,u< 60, and (0) HI : ,u #60. Hal/Aréa nzfé wry . ‘ . Y-go . 2t: kl/ffr l~f5 : PCPeJ‘eCf .l/gf/M)=p(‘7>€f-6‘4$‘ {/M‘) :P y‘” £1937:— Y/Jw > 9' {/My 16 GIQV§~¢M : Z> , 2% “7m, ) HI: <60 w y $ fl ’2 :«Lé‘z’r or Y< $3.3 :4 z I’fS :F’(\7< 583$ {/M) (2; 4 W) : 1° q/m: {6.) L4,: /UL=:-’“éO 6 E “ c‘f: MC {Zak/7 ZO‘OZy: L6] ede. - ' cf >7>6we or y<530 I {3 t 19(5") 6/.96 or >7<§<5°,0Lf l/M) P(>7>6I.qg, {/M) + P(>7<$‘8.07 ,4 , ( 5<:r‘«0‘“"~/"L 61.953‘fl )4—P Z4 59/ > Jig : NZ ma. 8 Hal/1‘10 H ._fl#lo >140 :196 (,4 52*’:( 20-02.? ReJecé JV? 3? 6’"! "‘ or F‘gq . {I p y > ’0 +. m or :7 n :LXL/ ?_€v\'\ 59mm: P(Io— f. <y<lo+ m] “ $.8‘1M :37 \ :F(IO m ’2. <Z<IO+T—,Z) g/m V/m g M (00 0”” 2 0 08 (e) Shrug/[2.526 m 5,6. (x) a; 50-01 6:, 9&10. Larsen & Marx p. 378, Question 6.4.10 modified. ~39 £7(5)2C>i\)€ ’4‘ / s>o m=A=I HI: A>I Efificfi :fi yaV¢ (GA Ac o<= TOO/2 (A6 M:;): fC—dej : [~63 V =00! Etd‘ect" rf w’z k. Maize w~3ammq(V/\3 (a) x: P(Wik/A:{):f1£w(w}dw k WL‘grfl fifwfw) {.r {£14 pol—7’ 016 SQMMq(V, I )_ 71:7ng p<-« ghqn_é;{_e °1£ SD‘W‘MR (‘11!) M3517 4w example Mini‘éGE‘ 0(20’0: :; k:;';f Ff}: P(Wi ¥.;¢: IA) = f # (w)0(v« ?.%y N were {NM m Feat one ammo/m Calm/Mate uscmj CMM-FFG6 140?“ my MTMéc‘é Rm.“ (at A VOM‘d i [1.02) The She of Y c; x:P(>1;.€r/9=0)=0.0r The fiza of Y c‘; Poi-+53} c: (6:0) 2. ED {:L‘M- Z-g-I (Larsen «3. Marx) (Afsume 6:0) DO )2 _ (2;) .s— a! 'RNOA’ “ifs/l ‘FHZON :) a fify(z)—£y(w-a) > o (a) 19— cgéswd and 64W~Z<Qfl (=3 Qazcafland w~e~w<z<w~e Ci} (-11: wE(ze/Ze+0; 4y (Z)£y(vJ-%\ >0 VJth 9< E {W—e— y 2 (a) MC WQEZGHIZG‘PZ): I (z)£y(w~z\>o WLVQW w_e’~(< Z<g+§ '73 2' IN"; 15 1d; 1 Za<w<ZG+I 2 6" O{Llerw752) 6—H - f1d2 «HE 19+~lswcze+z Mew w—ae 29<w<ze+I : (O GTEIAQIWTs-a) 26+z—w 26+Isw<29+L 2. P(v.+y7_>}c {9:0} : ICZ—wvdw :15 1sICsZ C Sa‘ve for )2 ...1¢,/ szx <. (5) Fat {La jinx? ~€es~6 wa (acme o In? Qs~0,or 1-73 2” P(>’I > arm-[e] = €+aos~ 7-; “0.051 esaflr 1 MC 9~>0fi§ Msinj «éLa daft“ of W {mm (a) we, fie-é :-[g=P(w>ic)r O “f 950%)“ (2.9+2.~Jc):/Z PF (‘C/Z)~!<~95(IC“)/Z “ (It—25072 r4 (Ind/Zoe: e C/a 1 r4 ’9; < 9 (C3 Pram H49. graph -:+ [5 deem 'éLa‘E' T1 R5 more Powar‘fia{ T/ér‘ a9 wear- 0 éu‘é Ya F5 mare PovJU-‘A( 7£0nr (arafir‘ 95- QUESTION 11 0. ‘_ 0‘8 0‘6 0 A4 0.2 0‘0 I l n I n r r -1.0 :05 0.0 0,5 1.0 15 2.0 theta‘seq Plot from part (c). QUESTION 7 mu.seq mu.seq The plots from parts (a), (b) and (c) of question 7. QUESTION 9 and 10 2 g f '6— ,I $ ! CE; I ‘c 1 .CD Q (Q , E <0, = D {I g a .5 :. >~ Lo" 5 b, q: S Yr, 6 E c E g» c; <'\! <'\l o o o , Q J <:> O I I I I I I I I I I 0 2O 4O 80 80 1 00 O 5 ’l O 'I 5 20 lambda‘seq lambda‘seq The plot from part (e) of question 9 to the left and the plot from part (g) of question 10 to the right. ...
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