PRINCE SULTAN UNIVERSITY Department of Mathematical Sciences Final Examination First Semester ( ) STAT 271.
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1 PRINCE SULTAN UNIVERSITY Deprtment f Mthemticl Sciences Finl Exmintin First Semester ( ) STAT 71 Student Nme: Mrk Student Number: Sectin Number: Techer Nme: Time llwed is ½ hurs. Attendnce Number: 40 Write dwn yur nswer in the spce prvided underneth the questin. Yu my use prgrmmble clcultr nd/r the ttched frmul sheet. Use if nt specified. Z 0.10 Z 0.05 Z 0.05 Z 0.01 Z Attempt 5 questins. Questin 1: A cmpny specilizing in fst fd prducts ffers sndwich in five different styles (A, B, C, D, nd E). A rndm smple f n 500 sles hs prduced the fllwing dt: Style A B C D E Number sld (bserved cunts) (Hint: If there is n style preference, then p 1 p p3 p4 p5 1/ 5 ). (1) If there is n style preference, clculte the expected number sld (expected cunt) fr ech style, nd fill in the fllwing tble: Style A B C D E Observed cunts ( O ) Expected cunts ( E ) i i () Test the hypthesis tht there is n style preference t the level f significnce. (Yur discussin shuld include the null nd the lterntive hyptheses, the vlue f the test sttistic, the rejectin regin, nd yur cnclusin.)
2 STAT 71 Finl Exmintin First Semester Questin : 900 peple were interviewed t study the reltinship between their sex nd smking hbit. The study hs prduced the fllwing dt: smking hbit Dily Smetimes never Sex Mle Femle (1) If the smking hbit is independent f the sex f the persn interviewed, clculte the expected number f peple (expected cunt) fr ech cell, nd fill in the fllwing tble: smking hbit Sex Mle Femle Dily Smetimes never () Is there sufficient evidence t indicte tht the smking hbit is dependent n (nt independent f) the sex f the persn interviewed? Use level f significnce. (Yur discussin shuld include the null nd the lterntive hyptheses, the vlue f the test sttistic, the rejectin regin, nd yur cnclusin.)
3 STAT 71 Finl Exmintin First Semester Questin 3: A study ws cnducted t determine the effects f bsence n students' chievement in prticulr Mth curse. A ttl f 10 students prticipted in the study. At the end f the semester, the number f bsences () nd the finl mrk (Y) f ech student were recrded. These results were btined: Y Assume the reltinship between Y nd is given by the fllwing simple liner regressin mdel: Y= +. Use Appendix (A) t slve the fllwing questins. () Find the lest-squres estimte f nd. (b) Write dwn the estimted lest-squres line (predictin equtin). (c) Use the predictin equtin t predict the finl mrk fr student wh hs been bsent fr 11 times. (d) D the dt present sufficient evidence t indicte tht Y nd re linerly relted? Explin yur nswer. (e) Test H : 0 ginst H : 0 (use 0.05). (f) Find 95% cnfidence intervl fr. (g) Clculte the cefficient f crreltin ( r ) between nd Y. (h) Clculte nd interpret the cefficient f determintin ( R ).
4 STAT 71 Finl Exmintin First Semester Questin 4: In rder t study the reltinship f dvertising nd cpitl investment n crprte prfits, the fllwing dt, recrded in thusnds f Riyls cllected fr ten medium-sized firms within the sme yer. The vrible Y represents prfit fr the yer, 1 represents cpitl investment, nd represents dvertising expenditure. Y We nlyzed these dt using Excel bsed n tw mdels; mdel (1): y 0 1 1, nd mdel (): y 0. The Excel printut is given in Appendix (B: B1 nd B). () Fr mdel (1), find nd interpret the vlue f the cefficient f determintin. (b) Fr mdel (1), test H 0 ginst H : 0 fr sme j. (use 0.05). : 1 j, (c) Fr mdel (1), test H : 1 0 ginst H : 1 0. (use 0.05). (d) Fr mdel (1), test H : 0 ginst H : 0. (use 0.05). (e) Which mdel d yu prefer; mdel (1) r mdel ()? Why? (f) Fr the mdel yu hve chsen in prt (e), write the predictin equtin (estimted equtin) relting Y nd the predictr vrible(s). (g) Using the mdel yu hve chsen in prt (e), estimte the yerly crprte prfits fr medium-sized firm whse cpitl investment ws 0 thusnds Riyls nd whse dvertising expenditure ws 40 thusnds Riyls.
5 STAT 71 Finl Exmintin First Semester Questin 5: (I) Stndrds set by gvernment gencies indicte tht Americns shuld nt exceed n verge dily sdium intke f 3300 milligrm (mg). T find ut whether Americns re exceeding (i.e., t hve mre thn) this limit, smple f n 00 Americns is selected, nd the men nd stndrd devitin f dily sdium intke re fund t be 3500 mg nd S 1000mg, respectively. Use 0. 05t cnduct test f hypthesis. Arrnge yur nswer s fllws: () The null nd the lterntive hyptheses re: H : H : (b) The vlue f the test sttistic is: (c) The rejectin regin fr the test is: (d) The cnclusin is: (II) The recrds f cmpny shw tht 1 30 men in smple f n mle emplyees versus 10 wmen in smple f n 50 femle emplyees hld highrnked psitins in the cmpny. D these dt present sufficient evidence t indicte tht the prprtin f men hlding high-rnked psitins is different thn the prprtin f wmen hlding high-rnked psitins? Use t cnduct test f hypthesis. Arrnge yur nswer s fllws: () The null nd the lterntive hyptheses re: H : H : (b) The vlue f the test sttistic is: (c) The rejectin regin fr the test is: (d) The cnclusin is:
6 STAT 71 Finl Exmintin First Semester Questin 6: (I) Tw rndm smples f sizes n 1 =10 nd n =10 bservtins were selected independently frm tw nrml ppultins with equl vrinces. The fllwing results were btined: 1 st Smple nd Smple Smple men ( ) Smple vrince ( S ) 0 4 (1) D these dt indicte tht there is difference between the mens f the tw nrml ppultins? Use =0.05. Arrnge yur nswer s fllws: () The null nd the lterntive hyptheses re: H : H : (b) The vlue f the test sttistic is: (c) The rejectin regin fr the test is: (d) The cnclusin is: () Cnstruct 95% cnfidence intervl fr 1. (II) A study hs been mde t cmpre the men mnthly slry f the emplyees in 4 cmpnies (A, B, C, nd D). A cmpletely rndmized design hs been used fr this study. The ANOVA tble f this study fllws (with =0.05): Surce f Vritin SS df MS F P-vlue F crit Tretment Errr Ttl 19 () Cmplete the ANOVA tble bve. (b) D the dt prvide sufficient evidence t indicte difference in the men mnthly slries mng the cmpnies? Use =0.05.
7 y STAT 71 Finl Exmintin First Semester Appendix (A) fr Questin 3: SUMMARY OUTPUT Regressin Sttistics Multiple R R Squre Adjusted R Squre Stndrd Errr Observtins 16 ANOVA df SS MS F Significnce F Regressin Residul Ttl Cefficients Stndrd Errr t Stt P-vlue Lwer 95% Upper 95% Intercept x x Line Fit Plt y Predicted y x
8 STAT 71 Finl Exmintin First Semester Appendix (B) fr Questin 4: (B1) Output fr mdel (1): y SUMMARY OUTPUT Regressin Sttistics Multiple R R Squre Adjusted R Squre Stndrd Errr Observtins 10 ANOVA df SS MS F Significnce F Regressin Residul Ttl Cefficients Stndrd Errr t Stt P-vlue Lwer 95% Upper 95% Intercept (B) Output fr mdel (): y 0 SUMMARY OUTPUT Regressin Sttistics Multiple R R Squre Adjusted R Squre Stndrd Errr Observtins 10 ANOVA df SS MS F Significnce F Regressin Residul Ttl Cefficients Stndrd Errr t Stt P-vlue Lwer 95% Upper 95% Intercept
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