bilkent statistics.2pdf

# bilkent statistics.2pdf - h [gffﬂ 1/5 (way = Date: May 2,...

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Unformatted text preview: h [gffﬂ 1/5 (way = Date: May 2, 2008 Time: 18:00—19:50 Instructor: Dilek Gﬁveno Do NOT use your mobile p ne . -. Write your name on each quest' npage and on formula page. Do NOT forg to return the bles and the formula page, as well. *9: ****** ********* _ 1. Let X be the time to failure of a certain hinge, for a given 3L, X is an exponential random variable with parameter it. From prior experience we are led to believe that 1 is a value of an exponential random variable with probability density f(1) = 2a“ a > 0 a) Find the posterior density of it. (18 points) b) Find the Bayes estimator of 7L. (7 points) 4‘" (20-25” >\>o 0') X>O )1 -' ' 4A "A -AMH) ._) dog”: 2.?- Ae x : er x>o, A>o a” -AOV—z) I _ A: q j“): 2A2, J/X (XHl/MC’ 7+2 Old 0 at I (Xfllcblzoé4 00‘: ML?— * f 9— ua—q 6&4 “ 0 sz sz do " 2 —— 2 xbo 2. - [Ueqqlqzﬂlﬂ(2)—(sz)z : xrzY— -' 6+2) ( 0' - exam-2.3 L 73—”) Was/Lula/ (la/'94? 0/ )l i 1 ' (Hz? -AM—H.) == A09»ng )‘30 I Name: ...... . . . . . . .. 2. A commonly prescribed drug for relieving nervous tension is believed to be only 60% effective. Experimental results with a new drug administered to a random sample of 100 adults who were suﬁering from a nervous tension Show that 70 received relief. a) Is this sufﬁcient evideme to conclude that the new drug is superior to the one commonly prescribed? Use P-value to make decision. Let (120.05. (13 points) b) Calculate the power of the test when true proportion of relieves with the new drug is 0.69. (12 points) a) #9" /:0.60 ’5‘: \$20 :0’20 HﬂIv/a>0,60 Mo 2d: 0'7_0‘6 :w22.04 c 0 g- ,4(z.04):0,s_0.4?93= 0,0207 L—m ’ ) Ava/(u _ ﬂ(2>z.o4 LHOJWCL/Ja HDJW r Swine. ﬂl/Wc 20,020? 40.05” WI. x7“, 00(3) 1‘5 5:2 prr all 91-:0,OS _ b) (7‘- : 0’05- 2047 Zara; 5 z' ’ 0‘ 6 > / 64 g ‘ lam Afr I , We, fits/f Ho ﬁgwtia’é) /00 . H. ,égl A30,6+//,64s)\/,07§g (0 05+ ﬁnite) &,S#0.0;LS"3: Name: ................. .. 3. A large automobile manufacturing companyis trying to decide whether to purchase brand A or brand B tires for its new models. To help arrive at a decision, an experiment is conducted using 12 of each brand. The tires are run until they wear out. The results are Brand A : )7, = 37900 kilometres, 31 =5100 kilometres. Brand B 1 3?, = 39800 kilometres, 31 = 5900 kilometres. Assuming the normality of the populations, a) Test the equality ofthe variances. Let a = 0.05. (10 points) b) Is there any difference between two brands of tires? Using the result in part (a), test at a = 0.05. (15 points) a) Alla/72:12. 7. 7— V —— Z ﬂex/7:0: of (7171‘! F 3890001=6€2=43§ HA, 9533.67“ er JEL>1 54th F :/,34 §0{//,/2):2,g2) 054.3% M # rélA/F [La F (//,//):2-5??—* ' 0,05 [72% Ho, 60,7050qu H! .L Vex/lwa m aft/ave wé p¢=o.05'_ 5) H0" ﬂip/(1:0 ﬂSJ‘un/I/f/IJ aft/wt? “Yd l’"M’t’i-"‘-ﬂ"-4’—S #A"ﬂ/”H2—7£O {Ag PM”; (so) 2 z 7' (7/)(5/0OD1t0/lf5900)?‘ : M (3/60 +9.90 ) 5/99th '— /21L/2—2 2'2 : 304/0000 SFQJZLJ 5" 55/4” 53 398,60_3I;L300 g /3c70V6 210,574? __ ﬂ Name: .................... .. 4. In a sh0p study, a set of data was collected to determine whether or not the proportion of defectives produced by workers was the same for the day, evening, or night shift worked. The following data were collected: Shift Da Evenin Ni ht a Defectives 45 (5‘? 55 56- ? 70 55.3 /7—0 Nondefectives 905 K 3 890 870 K 456 5 737421 930 945 940 28735 Determine if the proportion of defectives is the same for all three shifts. Test by allowing type I error to be present 2.5 % of the time. 4 .2665 /¢o _ : ﬁzggg; ﬂ: 2335 N F) 2835‘ Unoéx 19/0, _ (sso)(/?a) _57 506’) 2833 3 (94\$)[/7_0 _55,9_ 506;). 2873: : Mg“ 506%) 2935 ﬂ (930) (2565) 2 5,93 E (X20? 23's: EKXZZ) .7 (94962660 2 mac? 522/35 EKX ): (940 (2555) -; 57573,?- ” ,zirss 2 Z 2:306: (45—3?)11_M+C?02L53_), 71— £2392 57L 5} 56.3 93 l (gap—92m? Jr W: 5.23 7" W 57373.? 2 1 __ 34m, 224:5,2994 0‘0£§)-7:38'o£3/w14 ...
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## This note was uploaded on 11/08/2011 for the course MATH 332 taught by Professor Feritöztürk during the Spring '05 term at Bilkent University.

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bilkent statistics.2pdf - h [gffﬂ 1/5 (way = Date: May 2,...

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