Hypothesis Test for m with unknown standard deviation

# Hypothesis Test for m with unknown standard deviation - A r...

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Unformatted text preview: A\ r dDM-V(3(U.Ca“ “a \ (uncde memo! Wd’ “xx ST5 2610: Quantitative Methods Spring 2014 ‘2‘, Exercises: Hypothes Tests for p (0 Known) 1. Suppose that previously the average assembly time for the Omega Motors Buzz was 38 hours. The standard deviation for the process is known to be 3;; _1.2 hours. Modifications have been made to the process in hopes of reducing the average assembly time. A simple random sample of 35 Buzz vehicles assembled using the "improved process” have a sample mean assembly time of 37.4 hours. Assume that the standard deviation for the process remains at 1.2 hours. Does this give statistical evidence that the changes have reduced the average assembly time. Test using level of significance .05. (\e 35 32 : 31+ 0": 1.2. m, “M ﬁnpnvt‘mmt-l u isthe owtratﬁ asscmuy NM 0 Ho: Mg 3 5 8 H.: K‘ 5 X Level of significance: 5‘ : .05 Test Statistic: 2 = 37' 4" 58 Rejection Region: 16363 2 1- - “:45 , 1 7436 p-value:P 5-39 ': .OQLS . (2 b) KCICU no 0H as =.o\$ Conclusion: i,ng in: average asscmbv Him is rwdrd Give a 95% conﬁdence interval for p. 8y how much has the assembly time been reduced? 2. Following maintenance and calibration, an extrusion machine produces aluminum tubing with mean 2.500 inches. The process standard deviation is 0' 2.027 inches. As the machine functions over an extended number of work shifts, the standard deviation remains unchanged, but the combination of accmnulated deposits and mechanical wear causes the mean diameter to drift away from the desired 2.500 inch target value. For a recent random sample of 36 tubes, the mean diameter was 2.509 inches. At level of signiﬁcance .01, is there statistical evidence that the machine needs maintenance andcalibration? nt 35 92‘: 0" = .023 u ism mam-K d‘amricr (vigil mu poduwa by wt was W [(3 3.50) "ozK'fa'a’o Leveiof significance: 04 7— ,o‘ What is the probabith data will lead us to shut down the process unnecessarily? What type of errorwomdthisbe. ypel rTypeil? —, al’Cz‘ clam) Regection region: 2 (— ~2mc¢ 2 )2 cos Test statistic: v Fm“; -3539 \$1,540 _ PW -.‘.,,\\ ~, raCOJQB): Carries-on: \ ’z‘ r (3.507. .2600 @1le “N... ~‘~~'~u.4. ﬂ. ‘ =300/ M/ 0.1% WI 7". ‘ ' «1% “HA5 w. .26 Sammy" om 838 9.3 3 m 33E3é~m cmm .m «38¢ 8 cm 8 0:28? 9: Sm 2:958 E: .30 3mm a< Sm azsm 9683 3:02 m 3036. EMS—USS: <33 38: Hop 95an 2:2. 3m 88% a o . . . . u I. u . n 382% 083%. .25 9083 Manama Qmsmco: a o. .05 0:33. X ‘ \D‘ NVN. ON 5 m 98:2 8:22 33229 318832 8 3mm 2 2:? m8 \$333 2 3303 :03 3m 3232mm uqoncnzo: man :6: 83838 555:3. .25 825 .ﬁoﬁ 3m .28” \$285 96 mm<m3 \$.92. 01..” . 0 Houm Hobu HOPN Hohm Hoam Houn— Hohh Hobw Hob» Hohm m. mm<m m .38 nomamanvm 382m. «9‘ 3m uSnUM «WW: £4. mmoMMS 63 ‘0. w”: bkk \O . wmuu o4». \. No. . Q a. . 44M :vzpmoub: r\\ a. cmm <05 nesmqmanm 382m: 8 8m" IouhuHoN mention. myoca Em Emma" 25 3:: 36038;» 5:2 mm :5 _m<m_ 0% «523838 03:; 3mm. , 6 meQ :0 _- 2.32.22 .2: .1 b m u . ow, ...
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