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Nonparametric Statistics Questions and Solutions

Nonparametric Statistics Questions and Solutions - Chapter...

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Unformatted text preview: Chapter 13 Nonparametric Statistics 13- 1 Overview 13—2 Sign Test P 695 1,3,9,11 13—3 Wilcoxon Signed — Ranks Test for Matched Pairs P 702 1,3,5,7 13~4 Wilcoxon Signed —— Sum Test for TWO Independent Samples P 708 3,4 13~5 Kruskal-Wallis Test P 716 1,4,5 I 13—7 Run Test for Randomness P 736 5,7,9,13 Overview Sign Test P 695 1,3,9,11 1.; Tasting Ema Difi'farence Baéwaen Raymfiad mg Mtéasuresci Female fléfiighmmés sat-aim}. wait ’mpmmd fiai‘ghti} and measurmi hfiigfkfifi far a Samg-Ee (if mafia stark.» tics stadants. 'Listeéi heart are .haightsz {in inchm} cafiemfiad {mm a rand-em samplia foemaié SMfiSfiCS sindanm Is time; suffigémzt Evidence £10 suppert Elle: c‘iaim. mm thaw. ES 3 fiifiammm 'bmwmfl mpflfiad and maaamafl iwights: wf fiamam Statiafiw awaits? Use 3. {31,33 Eignificaflm lavel, 5.; g4 59 :56 W35 W . 3. Naming? mam: Saw}? £31? 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Bumbag far the: results given. in the ffll‘lfiwing saqumca W’ima would a Eack eif ramiamnasa 1113335111 is tha gamer? ’I‘t') the Gains"? GDEEEEOGEQEOQQOOGEGE '3’. Testing; far Ramfiaflumss in: Dating Er-aspacts firm has had {éiffimglty gag-fling dates with women! 3.0 ha is abandflnifig his stratagy of caraful seEactia-n anti re‘pianing; it with a tiesgemm fanfatagy £3115 ffifid‘om whammy 111 pursumg dateg with randumiy fi-filfi'ctfid wnmtm field iiimis that 301m 0? than: are unavailabfe bananas may are marrififi Fred; when has an flammauca of time £01“ gush aafiivi» 9.; “flaming £01” Rmdammaa 03‘? Freaicifintiai Rafi-{21:13:52}, Winnem Fm: a mwm mqmma 0&3 pmsidmfiaifi eiwtims, the; yuliticai. party of the winner is. indicated by E3 fior Democrat: am} Bi far Repnbiicafih 139% it appear “mat we glam Harms-rat and Rafiubiicm mmiidafiag in a fifiqufinm that. is mama}? 31.3.11}R‘fiRRRflBflRRRflflfiBBRRED RRDRRRIDQ figs, magma and afia‘i‘gzm his e-bfimvaflma Sivan tiara msnits lismd beffiow {Wham M {ifififlfifiifi maxim mini S mamas aizzgia}, what filwid Wad fits-mama: about that ranéammss at“ that wa'mm Em s-amcts‘? MESS.SSS-MMSM3MMSSMMSSMMMMMMMS 13 Tasting "Em Rmmimmagg {if Quid. and Emma. flights in Pi; A NW year-k fimas: articia about $16: flaicuiatian of fiacfinal pfifims of 7; namd Thai “mathamafichng are pretty sum mat the» digits 0? *2? am infiimimgaishabig “from an}! madam sequamfif’ {Siva-3:1 infiéaw am the first 13E? dadmw {31mm of an. Tia-SF: fear. rmdamw mass 0f mid (U) and SVEE {H} digits. 141.5926fi3539’W32384626¢33833$95828341.97} 139-31393735 1&332%9?49$¢5923{}?81 5442152862839? 3%2803482534211?067§ Chapter 13 Answers Section 13—2 1. The test statistic of x = 3 is not less than or equal to the 9. ”ii. 13. entice! value of 1. There is not sufficient evidence to sup» port the claim that there is a difference between report— ed and measured heights of female statistics students. . Convert x a 301 to the test statistic z = ~42.61. Criticai value: 2 = ~1 .645 (assuming a 0.05 significance ievel}. There is sufficient evidence to support the claim that the majority of people say that they voted in the election. . Convert x=i to the test statistic z== —5.32. Critical value: 2 = -1.645 {assuming a 0.05 significance Eevel). There is sufficient evidence to support the claim that the Coke cans have volumes with a median greater than 12 oz. . {instead of a right—tailed test to determine whether x = 18 is iarge enough to be significant, use a ieft—tailed test to determine whether x m 15 is small enough to be significant.) Convert x = 15 to the test statistic z m “0.35. Critical vaiue: z = ~1 .645. There is not suffi— cient evidence to support the claim that the median is greater than 0.9085 g. The test statistic of x a 1 is less than or equal to the critical vaiue of 2. There is sufficient evidence to warrant rejection of the ciaim of no difference between the right— and left~hand reaction times. Convert X m 8 to the test statistic am —2.83. Critical values: 2 m $2.575. There is sufficient evidence to war- rant rejection of the claim that the drinks had no effect on reaction tirnes. First approach: 2 = —1.90; reject Ho. Second approach: 2 = —1.73; reiect Ho. Third approach: 2 m 0; fail to reject Ho. 15. *,*, *, *, *,0,0,0,1,i.1,2,2,3,3 Section 13-3 1. Test statistic: T2 9.5. Criticai value: T m 3. Fail to reject the null hypothesis that both samples come from the same population distribution. 3. Test statistic: Tm 4.5. Critical vaiue: T m 21. Reject the null hypothesis that both samples come from the same population distribution. 5. Test statistic: T e 5.5. Critical value: T2 13. Reject the null hypothesis that both samples come from the same population distribution. There is sufficient evidence to support the claim that there is a difference between the two times. . Test statistic: T: 0. Critical value: T= 14 (assuming a 0.05 significance level). Reject the null hypothesis that both samples come frorn the same population distribu- tion. There is sufficient evidence to support the ciaim that the drug has an effect. . a. O, 27.5 b. 0, 637.5' c. 1954 Section 134 1 . p” = 577.5, 0;; a 56.358, H = 569, z = —o.15. Test statistic: z = -O.15. Criticai vaiues: z = $1.96. Fail to reject the nuil hypothesis that red and brown M&Ms have weights with identical popuiations. They appear to be the same. . [in = 350,0;1 = 17.321, 5’ m 96.5, 2 = —3.09. Test STE" tistic: z w ~3.09. Critical vaiues: z w "12.575. "There is sufficient evidence to warrant rejection of the claim that the two samples come from ldenticai populations. flag as 1314, 0'3 = 88.792, R a“— 1958, 2: 7.25. Test stew tistic: z m 7.25. Criticai vaiues: z M $1.86 {assuming a 0.05 significance level). There is sufficient evidence to support the claim that the two samples come from diffen ent popuiations. The sugar in reguiar coke weighs more. .pfi. =1330,cr,q a 94.383, Fr: 1153. 2a Min. Test statistic: z = —1.77. Criticai vaiues: z = $1.96 iassurn» ing a 0.05 significance ievel). There is not sufficient evi- dence to'support the claim that new textbook prices are different at the two colleges. 9. The resolts are the serne. ‘l. . z = 0.74; the test statistic is the same number with opposite sign. Section 135 Test statistic: H= 14.431. Critical vaiue: X2 a 7.815. There is sufficient evidence to warrant rejection of the ciaim that the different years have time intervais with identical populations. . Test statistic: H 2 4.234. Criticai vaiue: X2 = 7.815 (assuming a 0.05 significance ieveli. There is not suffi cient evidence to support the ciaim that left femur loads for the four car weight categories are not all the same. {They are not significantly different.) Test statistic: H = 6.631. Criticai value: x2 = 5.991. There is sufficient evidence to warrant rejection of the ciaim that the three samples come from identicai populations. '1'. $est statistic: H = 2975. Critical vaiee: x2 m 11.071. There is not sufficient evidence to warrant rejection of the cieim that the weights are the same tor each of the six different coior populations. 9. a. “the test statistic H does not change. b. The test statistic H does not change. c. The value of the test statistic does not change much {because the rank is used instead of the magnitude of the outlier}. r 3?. ST W 366; adjusted H m 14.431335 + 099868910, which is 14.479. Change is not substantial. Section 13 ~7 3. n1 2 10, n2 "—M 5, G m 3, 5% cutoff values: 3, 12; reject randomness. 3. n1 = 8, n2 m 12. G = 6, 5% cutoff valees: 6, 16; reject randomness. _ s. n. = 1’2, n2 m a. e m 10.5% cutoff values: a, 15; tel: to reject randomness. 7. R1 = 35, ti; = i3, G = 32, 5% cutoff values: 9, 21; fall to reject randomness. 9. n1 2 17, n2 m 14, (3 m 14, 5% cutoh‘ values: 10, 23; fall to reject randomness. 11. The median corresponds to July 2; n. = 6, n2 = 6, G e 2, 5% cutoff Values: 3, ii; reject randomness. 13. n, = 49, n: = 51, G n 48. Leg = 50.98, as a 4.9727. Test statistic: z 5—160. Criticai values: 2 = "£1.98. Feii to reject randomness. “:5. n1 = 34,171 = at, G a 3541.6 = 33.431, ch w 3.9909. Test statistic: z i 0.39. Critical values: z= $1.96. Fail to reject randomness. 17. Minimum is 2, maximum is 4. Critical vetoes of 1 and 6 can never be realized so that the nuii hypothesis of ren- domness can never be rejected. ...
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