Solutions Manual to accompany STATISTICS FOR ENGINEERS AND SCIENTISTS by William Navidi Table of Contents Chapter 1 ...............................................................1 Chapter 2 ..............................................................13 Chapter 3 ..............................................................53 Chapter 4 ..............................................................72 Chapter 5 .............................................................115 Chapter 6 .............................................................133 Chapter 7 .............................................................168 Chapter 8 .............................................................190 Chapter 9 .............................................................209 Chapter 10 ............................................................229 SECTION1.1 1 Chapter 1 Section 1.1 1. (a)Thepopulationconsistsofalltheboltsintheshipment. Itistangible. (b)Thepopulationconsistsofallmeasurementsthatcouldbemadeonthatresistorwiththatohmmeter. Itisconceptual. (c)Thepopulationconsistsofallresidentsofthetown.Itistangible. (d)Thepopulationconsistsofallweldsthatcouldbemadebythatprocess. Itisconceptual. (e)Thepopulationconsistsofallpartsmanufacturedthatday.Itistangible. 3. (a)False (b)True 5. (a)No. What is important is the population proportion of defectives; the sample proportion is only an approx- imation. The population proportion for the new process may in fact be greater or less than that of the old process. (b)No. Thepopulationproportionforthenewprocessmaybe0.10ormore,eventhoughthesampleproportion wasonly0.09. (c)Finding2defectivebottlesinthesample. 7. Agoodknowledgeoftheprocessthatgeneratedthedata. 2 CHAPTER1 Section 1.2 1. False 3. No. Inthesample1,2,4themeanis7/3,whichdoesnotappearatall. 5. Thesamplesizecanbeanyoddnumber. 7. Yes. Ifallthenumbersinthelistarethesame,thestandarddeviationwillequal0. 9. Themeanandstandarddeviationbothincreaseby5%. 11. The total numberof pointsscored in the class of 30 students is 30 (cid:0) 72 2160. The total number of points (cid:1) scoredintheclassof40studentsis40(cid:0) 79 3160.Thetotalnumberofpointsscoredinbothclassescombined (cid:1) is2160 3160 5320. Thereare30 40 70studentsinbothclassescombined. Thereforethemeanscore (cid:2) (cid:1) (cid:2) (cid:1) forthetwoclassescombinedis5320 70 76. (cid:3) (cid:1) 13.(a)Allwouldbemultipliedby2.54. (b)Notexactlythesame,becausethemeasurementswouldbealittledifferentthesecondtime. 15.(a)Thesamplesizeisn 16.Thetertileshavecutpoints 1 3 17 567and 2 3 17 1133.Thefirsttertile (cid:1) (cid:4) (cid:3) (cid:5)(cid:6)(cid:4) (cid:5)(cid:7)(cid:1) (cid:8) (cid:4) (cid:3) (cid:5)(cid:6)(cid:4) (cid:5)(cid:7)(cid:1) (cid:8) isthereforetheaverageofthesamplevaluesinpositions5and6,whichis 44 46 2 45.Thesecondtertile (cid:4) (cid:2) (cid:5)(cid:9)(cid:3) (cid:1) istheaverageofthesamplevaluesinpositions11and12,whichis 76 79 2 775. (cid:4) (cid:2) (cid:5)(cid:9)(cid:3) (cid:1) (cid:8) (b)Thesamplesizeisn 16. Thequintileshavecutpoints i 5 17 fori 1 2 3 4. Thequintilesaretherefore (cid:1) (cid:4) (cid:3) (cid:5)(cid:6)(cid:4) (cid:5) (cid:1) (cid:10) (cid:10) (cid:10) the averages of the sample values in positions 3 and 4, in positions 6 and 7, in positions 10 and 11, and in positions13and14. Thequintilesaretherefore 23 41 2 32, 46 49 2 475, 74 76 2 75,and (cid:4) (cid:2) (cid:5)(cid:11)(cid:3) (cid:1) (cid:4) (cid:2) (cid:5)(cid:11)(cid:3) (cid:1) (cid:8) (cid:4) (cid:2) (cid:5)(cid:9)(cid:3) (cid:1) 82 89 2 855. (cid:4) (cid:2) (cid:5)(cid:11)(cid:3) (cid:1) (cid:8) SECTION1.3 3 Section 1.3 1. (a) Stem Leaf 11 6 12 678 13 13678 14 13368 15 126678899 16 122345556 17 013344467 18 1333558 19 2 20 3 0.16 0.14 cy0.12 n e qu 0.1 e (b)Hereisonehistogram. Otherchoicesfortheendpointsarepossible. e Fr0.08 v ati0.06 el R 0.04 0.02 0 11 12 13 14 15 16 17 18 19 20 21 Weight (oz) (c) 10 12 14 16 18 20 22 24 Weight (ounces) 22 (d) 20 s) e 18 c n u o Theboxplotshowsnooutliers. ht ( 16 g ei 14 W 12 10 4 CHAPTER1 3. Stem Leaf 1 1588 2 00003468 3 0234588 4 0346 5 2235666689 6 00233459 7 113558 8 568 9 1225 10 1 11 12 2 13 06 14 15 16 17 1 18 6 19 9 20 21 22 23 3 Thereare23stemsinthisplot. AnadvantageofthisplotovertheoneinFigure1.6isthatthevaluesaregiven to thetenths digitinsteadofto theones digit. Adisadvantageis thatthereare toomanystems, andmanyof themareempty. 5. (a)Herearehistogramsforeachgroup. Otherchoicesfortheendpointsarepossible. 0.25 0.35 0.2 0.3 y y c c n n e e0.25 u u q0.15 q e e Fr Fr 0.2 e e ativ 0.1 ativ0.15 el el R R 0.1 0.05 0.05 0 0 18 19 20 21 22 23 24 25 26 15 16 17 18 19 20 21 22 23 24 25 Group 1 measurements (cm) Group 2 measurements (cm) SECTION1.3 5 30 (b) m) 25 c nt ( e m 20 e ur s a e M 15 10 Group 1 Group 2 (c)ThemeasurementsinGroup1aregenerallylargerthanthoseinGroup2.ThemeasurementsinGroup1arenot farfromsymmetric,althoughtheboxplotsuggestsaslightskewtotheleftsincethemedianisclosertothethird quartilethanthefirst. Therearenooutliers. MostofthemeasurementsforGroup2arehighlyconcentratedin anarrowrange,andskewedtotheleftwithinthatrange. Theremainingfourmeasurementsareoutliers. 7. (a)Theproportionisthesumoftherelativefrequencies(heights)oftherectanglesabove130.Thissumisapprox- imately012 0045 0045 002 0005 0005 024.Thisisclosestto25%. (cid:8) (cid:2) (cid:8) (cid:2) (cid:8) (cid:2) (cid:8) (cid:2) (cid:8) (cid:2) (cid:8) (cid:1) (cid:8) (b)The heightofthe rectangleoverthe interval130–135isgreater thanthe sumof theheightsoftherectangles overtheinterval140–150. Thereforetherearemorewomenintheinterval130–135mm. 18 15 9. (a) Frequency192 6 3 0 1 3 5 7 9 1113151719212325 Emissions (g/gal) 6 CHAPTER1 0.15 (b) 0.1 Density 0.05 0 1 3 5 7 9 1113151719212325 Emissions (g/gal) (c)Yes,theshapesofthehistogramsarethesame. 11. Anypointmorethan1.5IQR(interquartilerange)belowthefirstquartileorabovethethirdquartileislabeled an outlier. To find the IQR, arrange the values in order: 4, 10, 20, 25, 31, 36, 37, 41, 44, 68, 82. There are n 11values. Thefirstquartileisthevalueinposition025 n 1 3,whichis20. Thethirdquartileisthe (cid:1) (cid:8) (cid:4) (cid:2) (cid:5) (cid:1) valueinposition075 n 1 9,whichis44. Theinterquartilerangeis44 20 24. So1.5IQRisequalto (cid:8) (cid:4) (cid:2) (cid:5) (cid:1) (cid:1) (cid:1) 15 24 36.Therearenopointslessthan20 36 16,sotherearenooutliersonthelowside. Thereis (cid:4) (cid:8) (cid:5) (cid:4) (cid:5) (cid:1) (cid:1) (cid:1) (cid:1) onepoint,82,thatisgreaterthan44 36 80. Therefore82istheonlyoutlier. (cid:2) (cid:1) 13. Thefigureontheleftisasketchofseparatehistogramsforeachgroup. Thehistogramontherightisasketch ofahistogramforthetwogroupscombined. Thereismorespreadinthecombinedhistogramthanineitherof theseparateones. Thereforethestandarddeviationofall200heightsisgreaterthan2.5in. Theansweris(ii). 15.(a)IQR=3rdquartile 1stquartile. A:IQR=602 142 460,B:IQR=913 527 386 (cid:1) (cid:8) (cid:1) (cid:8) (cid:1) (cid:8) (cid:8) (cid:1) (cid:8) (cid:1) (cid:8) SECTION1.3 7 12 10 8 (b)Yes, since the minimum is within 1.5 IQR of the first quartile and the 6 maximum is within 1.5 IQR of the third quartile, there are no outliers, andthegivennumbersspecifytheboundariesoftheboxandtheendsof 4 thewhiskers. 2 0 (c)No. Theminimumvalueof 2235isan“outlier,”sinceitismorethan1.5timestheinterquartilerangebelow (cid:1) (cid:8) thefirstquartile. Thelowerwhiskershouldextendtothesmallestpointthatisnotanoutlier,butthevalueof thispointisnotgiven. 500 17.(a) 400 a) P M s (300 s e Str ure 200 ct a Fr 100 0 (b)Theboxplotindicatesthatthevalue470isanoutlier. (c) 0 100 200 300 400 500 Fracture Strength (MPa) (d)Thedotplotindicatesthatthevalue384isdetachedfromthebulkofthedata,andthuscouldbeconsideredto beanoutlier. 8 CHAPTER1 60 19.(a) 50 40 y 30 Therelationshipisnon-linear. 20 10 0 0 5 10 15 x x 1.4 2.4 4.0 4.9 5.7 6.3 7.8 9.0 9.3 11.0 (b) lny 0.83 1.31 1.74 2.29 1.93 2.76 2.73 3.61 3.54 3.97 4 3.5 3 2.5 ln y Therelationshipisapproximatelylinear. 2 1.5 1 0.5 0 5 10 15 x (c)Itwouldbeeasiertoworkwithxandlny,becausetherelationshipisapproximatelylinear. Supplementary Exercises for Chapter 1 1. (a)Themeanwillbedividedby2.2. (b)Thestandarddeviationwillbedividedby2.2. 3. (a)False. The true percentage could be greater than 5%, with the observation of 4 out of 100 due to sampling variation.