A. Suppose that the daily simple returns of a stock in one week were -0.4%, 0.8%, 1.3%, -1.5%, and 0.9%. What are the corresponding daily log returns? What is the weekly simple return of the stock?

B.  Please list out three types of Moments of a Random Variable and briefly explain why they are important for financial data.

C. The data file assignment_1.txt contains stock returns for “ge” (general electric), “vw” (value-weighted market returns), “ew” (equal-weighted market returns), and “sp” (Standard Poor composite index). The time span of the data ranges from Jan 1940 to Sept 2011. Please do following work within R/RStudio environment. 

(a) Compute the sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of each simple return series.

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(b) Transform the simple returns to log returns and redo part (a).

(c) Test the null hypothesis that the mean of the log returns of “ge” stock is zero. Use 5% significance level to draw your conclusion.

date           ge            vw            ew            sp
19400131      -0.061920     -0.024020     -0.019978     -0.035228
19400229      -0.009901      0.013664      0.029733      0.006639
19400330       0.049333      0.018939      0.026168      0.009893
19400430      -0.041667      0.001196      0.013115     -0.004898
19400531      -0.197324     -0.220314     -0.269754     -0.239541
19400629       0.061667      0.066664      0.066550      0.076591
19400731       0.067460      0.032230      0.036805      0.031062
19400831       0.011152      0.023962      0.023221      0.026239
19400930       0.043382      0.023028      0.037207      0.009470
19401031       0.007117      0.029705      0.049218      0.039400
19401130      -0.048057     -0.016348     -0.001669     -0.042419
19401231       0.007605      0.006811     -0.018789     -0.002828
19410131      -0.003774     -0.040505     -0.007317     -0.048204
19410228      -0.003788     -0.014839     -0.019409     -0.014896
19410331      -0.008365      0.009599      0.014308      0.004032
19410430      -0.104651     -0.053065     -0.057382     -0.065261
19410531      -0.012987      0.013858      0.010105      0.004296
19410630       0.143860      0.058683      0.066908      0.053476
19410731      -0.015504      0.059519      0.130139      0.054822
19410830       0.031496     -0.000463     -0.007180     -0.008662
19410930      -0.016031     -0.007494     -0.020448     -0.009709
19411031      -0.133333     -0.051786     -0.062030     -0.068627
19411129      -0.032579     -0.019367     -0.034209     -0.042105
19411231       0.022749     -0.046728     -0.081886     -0.045055
19420131       0.018779      0.007158      0.130814      0.013809
19420228      -0.041475     -0.024149     -0.017579     -0.024972
19420331      -0.077885     -0.065655     -0.052240     -0.067520
19420430      -0.026455     -0.043145     -0.046260     -0.043695
19420529       0.086957      0.061047      0.028879      0.063969
19420630       0.049000      0.025482      0.025086      0.018405
19420731       0.014493      0.034877      0.046405      0.031325
19420831       0.009524      0.018656      0.028304      0.007009
19420930       0.050943      0.026300      0.047557      0.026682
19421031       0.068182      0.067688      0.101294      0.064407
19421130      -0.004255      0.002500     -0.013177     -0.013800
19421231       0.054701      0.050416      0.035554      0.051668
19430130       0.114754      0.073303      0.168551      0.071648
19430227       0.047794      0.059920      0.130930      0.050621
19430331       0.055439      0.062077      0.112136      0.052727
19430430      -0.023490      0.006903      0.035466      0.000864
19430529       0.044674      0.057158      0.084513      0.044866
19430630       0.055263      0.016911      0.010979      0.019818
19430731      -0.081761     -0.046205     -0.064335     -0.054251
19430831       0.013699      0.012986      0.003373      0.010274
19430930       0.056757      0.024527      0.034867      0.023729
19431030      -0.058065     -0.012218     -0.003943     -0.013245
19431130      -0.047945     -0.058529     -0.088584     -0.075503
19431231       0.071223      0.063623      0.098730      0.058984
19440131      -0.010169      0.018072      0.045949      0.015424
19440229      -0.041096      0.003686      0.013018     -0.002532
19440331       0.035000      0.024417      0.041526      0.016920
19440429      -0.003484     -0.016341     -0.029289     -0.012479
19440531       0.010490      0.050955      0.066135      0.040438
19440630       0.061592      0.056171      0.104935      0.051012
19440731      -0.016447     -0.015151     -0.012724     -0.020801
19440831       0.016722      0.015927      0.030082      0.008655
19440930      -0.010526      0.000191      0.000252     -0.003120
19441031       0.036913      0.002504      0.000953       .      
19441130       0.016181      0.016456      0.023183      0.003912
19441230       0.015287      0.041224      0.069303      0.035074
19450131      -0.018987      0.019194      0.043353      0.014307
19450228       0.096774      0.064282      0.086339      0.061618
19450331      -0.043529     -0.038728     -0.056802     -0.046154
19450430       0.086957      0.077474      0.088844      0.087977
19450531       0.011429      0.018630      0.030017      0.011456
19450630      -0.027684      0.003422      0.036565     -0.003331
19450731       0.020528     -0.022095     -0.035068     -0.020053
19450831       0.086207      0.061123      0.065928      0.057981
19450929       0.032275      0.048051      0.062646      0.041908
19451031      -0.023256      0.039018      0.064522      0.030322
19451130      -0.018519      0.054546      0.097574      0.032432
19451231       0.038275      0.011763      0.024073      0.009889
19460131       0.057592      0.063309      0.094677      0.069700
19460228      -0.051980     -0.057852     -0.066906     -0.069467
19460330      -0.009922      0.058716      0.057922      0.046296
19460430      -0.023936      0.042899      0.052109      0.037611
19460531       0.087193      0.039864      0.054749      0.022388
19460628      -0.039599     -0.039140     -0.048887     -0.039103
19460731      -0.015789     -0.025465     -0.040842     -0.025502
19460830      -0.080214     -0.063922     -0.075327     -0.072940
19460930      -0.077907     -0.100202     -0.135552     -0.101502
19461031      -0.057325     -0.014164     -0.011814     -0.008021
19461130      -0.054054      0.001200     -0.002634     -0.011456
19461231       0.036429      0.050925      0.046908      0.042945
19470131       0.090592      0.015128      0.030197      0.023529
19470228      -0.038339     -0.011577     -0.007105     -0.014687
19470331      -0.045847     -0.017058     -0.030425     -0.016850
19470430      -0.021127     -0.047868     -0.081680     -0.038893
19470529      -0.010791     -0.009997     -0.037321     -0.008916
19470630       0.044364      0.053652      0.057096      0.052595
19470731       0.073944      0.041240      0.061670      0.036160
19470829      -0.036066     -0.017509     -0.017166     -0.027919
19470930       0.004082     -0.004419      0.005783     -0.013708
19471031       0.000000      0.024614      0.033156      0.021178
19471129      -0.041096     -0.018306     -0.029305     -0.028516
19471231       0.032857      0.030189      0.023863      0.020680
19480131      -0.038462     -0.037266     -0.016276     -0.039869
19480228      -0.050909     -0.043439     -0.059451     -0.046971
19480331       0.115709      0.082763      0.095843      0.077143
19480430      -0.031250      0.037775      0.040151      0.026525
19480528       0.204301      0.074581      0.087630      0.078165
19480630      -0.011310     -0.000177     -0.012534      0.002996
19480730      -0.069909     -0.050421     -0.053733     -0.053166
19480831       0.032680      0.003854     -0.001818      0.007571
19480930       0.000000     -0.029544     -0.042785     -0.030056
19481030       0.083333      0.060056      0.053201      0.067786
19481130      -0.118343     -0.090626     -0.106320     -0.108223
19481231       0.057047      0.032202      0.013703      0.030508
19490131      -0.016077      0.003043      0.017749      0.001316
19490228      -0.058824     -0.029464     -0.041302     -0.039422
19490331       0.065972      0.041521      0.059309      0.030096
19490430      -0.023102     -0.017866     -0.031490     -0.021248
19490531      -0.050676     -0.027440     -0.043168     -0.037313
19490630       0.003559      0.003093     -0.007713     -0.002114
19490729       0.068345      0.055845      0.062022      0.062147
19490831       0.003367      0.026592      0.026020      0.011968
19490930       0.010067      0.031831      0.043249      0.023653
19491031       0.006734      0.031224      0.039025      0.029525
19491130       0.070234      0.018842      0.009400      0.001247
19491231       0.078125      0.052102      0.070120      0.043587
19500131       0.047478      0.017283      0.040293      0.017303
19500228       0.048159      0.014635      0.016102      0.009971
19500331       0.012973      0.012198     -0.001770      0.004065
19500429       0.045946      0.040257      0.047443      0.045113
19500531       0.018088      0.043689      0.033185      0.039292
19500630      -0.066497     -0.057935     -0.075737     -0.058040
19500731       0.013774      0.016118      0.050635      0.008479
19500831       0.038043      0.050699      0.051892      0.032511
19500929       0.007330      0.048804      0.055013      0.055917
19501031       0.023684     -0.001109     -0.005504      0.004113
19501130       0.000000      0.028518      0.031622     -0.001024
19501230       0.057218      0.057703      0.084545      0.046130
19510131       0.095477      0.058239      0.076248      0.061244
19510228       0.025229      0.014434      0.011586      0.006464
19510331      -0.008949     -0.020949     -0.033890     -0.018349
19510430       0.016018      0.049613      0.040814      0.048131
19510531      -0.033784     -0.022624     -0.024919     -0.040571
19510629      -0.002331     -0.025324     -0.044929     -0.026022
19510731       0.059242      0.071166      0.063332      0.068702
19510831       0.067114      0.045082      0.047438      0.039286
19510928       0.041929      0.009177      0.023631     -0.000859
19511031      -0.083503     -0.022397     -0.023609     -0.013758
19511130      -0.004444      0.005923      0.007185     -0.002616
19511231       0.075893      0.034898      0.015248      0.038899
19520131      -0.021008      0.016906      0.017491      0.015566
19520229      -0.053648     -0.024983     -0.020650     -0.036454
19520331       0.088435      0.045586      0.028864      0.047721
19520430      -0.037975     -0.048900     -0.044936     -0.043086
19520529       0.046053      0.032874      0.024515      0.023156
19520630       0.067086      0.039283      0.030728      0.046102
19520731       0.001988      0.011482      0.010652      0.017628
19520829       0.001984     -0.006584      0.000056     -0.014567
19520930       0.013861     -0.018991     -0.015160     -0.019577
19521031      -0.015810     -0.005456     -0.011717     -0.000815
19521128       0.128514      0.058795      0.055644      0.046493
19521231       0.046263      0.031210      0.022641      0.035464
19530130      -0.051546     -0.001342      0.024706     -0.007151
19530227       0.000000     -0.001711      0.012031     -0.018196
19530331       0.003623     -0.013417     -0.010486     -0.023552
19530430       0.027372     -0.027474     -0.024027     -0.026493
19530529       0.024867      0.007141      0.005896     -0.003249
19530630      -0.005199     -0.016655     -0.031671     -0.016300
19530731       0.031690      0.025329      0.017571      0.025269
19530831      -0.034130     -0.044092     -0.051874     -0.057778
19530930       0.045936      0.003053     -0.011005      0.001286
19531030       0.114334      0.047090      0.037834      0.050964
19531130       0.108729      0.028267      0.021317      0.008965
19531231      -0.011173      0.000768     -0.015444      0.002019
19540129       0.062857      0.052460      0.071683      0.051189
19540226       0.079301      0.017482      0.013576      0.002684
19540331       0.074720      0.037251      0.029150      0.030210
19540430       0.153216      0.042851      0.016373      0.048998
19540528      -0.047667      0.031569      0.043151      0.032909
19540630       0.185942      0.011477      0.012275      0.000685
19540730      -0.043478      0.050368      0.071989      0.057172
19540831      -0.056818     -0.022516     -0.009175     -0.034003
19540930       0.063855      0.064304      0.044308      0.083138
19541029      -0.037143     -0.016211     -0.006860     -0.019499
19541130       0.086053      0.095289      0.092199      0.080808
19541231       0.030601      0.055263      0.087724      0.050818
19550131       0.064171      0.006994      0.014124      0.018066
19550228       0.047739      0.031280      0.042781      0.003549
19550331      -0.042686     -0.001122      0.000530     -0.004897
19550429       0.065657      0.032281      0.022598      0.037726
19550531      -0.018957      0.011856      0.007814     -0.001317
19550630       0.034300      0.065800      0.034694      0.082300
19550729      -0.035294      0.020283      0.008001      0.060687
19550831       0.034146      0.004250      0.005764     -0.007813
19550930      -0.049057     -0.002034     -0.007751      0.011348
19551031      -0.065000     -0.025728     -0.017815     -0.030456
19551130       0.149733      0.071558      0.055257      0.074870
19551230       0.083721      0.016437      0.022836     -0.000659
19560131      -0.060606     -0.027987     -0.020746     -0.036500
19560229       0.073733      0.039532      0.033613      0.034687
19560329       0.100858      0.068175      0.051383      0.069255
19560430      -0.031434      0.005093      0.003827     -0.002063
19560531      -0.070994     -0.049186     -0.039964     -0.065730
19560629       0.074236      0.037157      0.021712      0.039159
19560731       0.047131      0.050753      0.039967      0.051522
19560831      -0.039139     -0.030342     -0.018161     -0.038064
19560928      -0.079430     -0.049677     -0.035938     -0.045464
19561031       0.066964      0.007221      0.007063      0.005072
19561130      -0.008368      0.004611      0.005277     -0.010970
19561231       0.025316      0.034934      0.023122      0.035271
19570131      -0.107884     -0.032051      0.003613     -0.041783
19570228       0.030233     -0.018698     -0.023299     -0.032648
19570329       0.060948      0.024087      0.022499      0.019649
19570430       0.087983      0.045059      0.025909      0.036953
19570531       0.053254      0.036599      0.022263      0.036948
19570628       0.033708     -0.005107     -0.006747     -0.001265
19570731       0.018248      0.008920      0.005610      0.011400
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19570930      -0.070881     -0.057622     -0.052982     -0.061920
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19940331      -0.044176     -0.045795     -0.045962     -0.045746
19940429      -0.047500      0.009478     -0.011728      0.011531
19940531       0.044619      0.009360     -0.000831      0.012419
19940630      -0.055578     -0.027909     -0.028182     -0.026812
19940729       0.080429      0.030633      0.015778      0.031467
19940831      -0.012407      0.042597      0.036756      0.037643
19940930      -0.025427     -0.018363      0.004865     -0.026898
19941031       0.015584      0.014520     -0.003305      0.020834
19941130      -0.058824     -0.037219     -0.040741     -0.039505
19941230       0.117609      0.012609     -0.013424      0.012299
19950131       0.009804      0.020399      0.027860      0.024278
19950228       0.063107      0.039615      0.028369      0.036074
19950331      -0.006210      0.027041      0.019518      0.027329
19950428       0.037037      0.025048      0.026976      0.027960
19950531       0.035714      0.034007      0.020270      0.036312
19950630      -0.020948      0.031173      0.049917      0.021279
19950731       0.046563      0.040783      0.054708      0.031776
19950831      -0.002119      0.009305      0.032043     -0.000320
19950929       0.089766      0.036362      0.026400      0.040098
19951031      -0.007843     -0.011317     -0.041473     -0.004979
19951130       0.061265      0.042708      0.016659      0.041049
19951229       0.079479      0.015191      0.008928      0.017444
19960131       0.065972      0.028144      0.034657      0.032617
19960229      -0.016287      0.016310      0.032305      0.006934
19960329       0.037550      0.010927      0.024086      0.007917
19960430      -0.008026      0.025511      0.058049      0.013431
19960531       0.071197      0.026800      0.062615      0.022853
19960628       0.048338     -0.008298     -0.032167      0.002257
19960731      -0.046571     -0.053819     -0.079602     -0.045748
19960830       0.010638      0.032463      0.045634      0.018814
19960930       0.100271      0.053015      0.028753      0.054173
19961031       0.063187      0.013632     -0.020842      0.026131
19961129       0.074935      0.065502      0.024696      0.073376
19961231      -0.044279     -0.011358     -0.002604     -0.021505
19970131       0.046776      0.053449      0.063831      0.061317
19970228      -0.006039     -0.001144     -0.010299      0.005928
19970331      -0.030182     -0.044820     -0.049224     -0.042614
19970430       0.118388      0.042303     -0.021596      0.058406
19970530       0.087838      0.071624      0.085194      0.058577
19970630       0.076605      0.044145      0.043145      0.043453
19970731       0.082846      0.076502      0.048824      0.078123
19970829      -0.107843     -0.036267      0.027605     -0.057446
19970930       0.092068      0.058433      0.081737      0.053154
19971031      -0.050505     -0.034528     -0.026145     -0.034478
19971128       0.143133      0.030459     -0.022063      0.044587
19971231      -0.002707      0.017772     -0.023875      0.015732
19980130       0.056218      0.004529      0.015367      0.010150
19980227       0.003226      0.073230      0.060451      0.070449
19980331       0.112379      0.051324      0.046884      0.049946
19980430      -0.011603      0.010862      0.023243      0.009076
19980529      -0.021277     -0.025755     -0.042571     -0.018826
19980630       0.089955      0.031955     -0.029150      0.039438
19980731      -0.012517     -0.023264     -0.050546     -0.011615
19980831      -0.105521     -0.157666     -0.196383     -0.145797
19980930      -0.001719      0.063835      0.043245      0.062396
19981030       0.099764      0.074357      0.037827      0.080294
19981130       0.032857      0.061985      0.075912      0.059126
19981231       0.132503      0.063054      0.018861      0.056375
19990129       0.028186      0.038345      0.064848      0.041009
19990226      -0.043504     -0.038105     -0.042172     -0.032283
19990331       0.106293      0.037861     -0.001373      0.038794
19990430      -0.047458      0.049000      0.083900      0.037944
19990528      -0.034994     -0.020721      0.025134     -0.024970
19990630       0.111248      0.051021      0.038391      0.054438
19990730      -0.032301     -0.030635      0.007271     -0.032046
19990831       0.030390     -0.009985     -0.030607     -0.006254
19990930       0.058765     -0.022868     -0.014250     -0.028552
19991029       0.142857      0.062049     -0.001351      0.062539
19991130      -0.039668      0.036814      0.091409      0.019062
19991231       0.192392      0.083721      0.084830      0.057844
20000131      -0.136511     -0.039588      0.050610     -0.050904
20000229      -0.009355      0.031844      0.120436     -0.020108
20000331       0.178735      0.053523     -0.000429      0.096720
20000428       0.010442     -0.059466     -0.088504     -0.030796
20000531       0.005167     -0.039047     -0.057324     -0.021915
20000630       0.005931      0.051640      0.079228      0.023934
20000731      -0.026903     -0.017106     -0.019355     -0.016341
20000831       0.140948      0.075811      0.059257      0.060699
20000929      -0.014711     -0.051138     -0.040102     -0.053483
20001031      -0.049837     -0.024557     -0.066807     -0.004949
20001130      -0.095781     -0.102534     -0.118559     -0.080069
20001229      -0.029559      0.020299     -0.007035      0.004053
20010131      -0.040834      0.039524      0.225012      0.034637
20010228       0.011309     -0.099267     -0.074508     -0.092291
20010330      -0.096344     -0.070286     -0.072716     -0.064205
20010430       0.159341      0.083911      0.076441      0.076814
20010531       0.009685      0.010566      0.062201      0.005090
20010629      -0.005102     -0.017474      0.007720     -0.025004
20010731      -0.104410     -0.018316     -0.028407     -0.010772
20010831      -0.057931     -0.059095     -0.035009     -0.064108
20010928      -0.088336     -0.091543     -0.127801     -0.081723
20011031      -0.021237      0.027970      0.078103      0.018099
20011130       0.057402      0.078735      0.080809      0.075176
20011231       0.045714      0.017844      0.057742      0.007574
20020131      -0.073104     -0.016045      0.018179     -0.015574
20020228       0.041184     -0.021713     -0.033060     -0.020766
20020328      -0.027273      0.044688      0.074666      0.036739
20020430      -0.157543     -0.049654     -0.003169     -0.061418
20020531      -0.012995     -0.010478     -0.015519     -0.009081
20020628      -0.061336     -0.070251     -0.067310     -0.072465
20020731       0.108434     -0.081135     -0.107499     -0.078995
20020830      -0.063665      0.007965      0.006337      0.004881
20020930      -0.176451     -0.099965     -0.084490     -0.110013
20021031       0.024341      0.074926      0.042772      0.086436
20021129       0.074059      0.061275      0.117775      0.057070
20021231      -0.095133     -0.053316     -0.040159     -0.060333
20030131      -0.049692     -0.023392      0.006068     -0.027415
20030228       0.047537     -0.015390     -0.021448     -0.017004
20030331       0.060291      0.010325      0.009434      0.008358
20030430       0.154902      0.082762      0.098222      0.081044
20030530      -0.025467      0.063471      0.133177      0.050899
20030630       0.005923      0.016335      0.049741      0.011322
20030731      -0.008368      0.023112      0.061927      0.016224
20030829       0.039733      0.024966      0.047429      0.017873
20030930       0.014542     -0.009112      0.025239     -0.011944
20031031      -0.026837      0.060318      0.080930      0.054962
20031128      -0.011720      0.016594      0.038147      0.007129
20031231       0.087548      0.045528      0.038907      0.050765
20040130       0.085539      0.023048      0.065762      0.017276
20040227      -0.027059      0.015459      0.013720      0.012209
20040331      -0.061501     -0.010694      0.006293     -0.016359
20040430      -0.018676     -0.024231     -0.043590     -0.016791
20040528       0.039065      0.014125      0.002592      0.012083
20040630       0.047558      0.021582      0.022729      0.017989
20040730       0.026235     -0.037667     -0.051082     -0.034291
20040831      -0.013835      0.002713     -0.004725      0.002287
20040930       0.030192      0.020546      0.041594      0.009364
20041029       0.016081      0.017805      0.020836      0.014014
20041130       0.036342      0.048210      0.079929      0.038595
20041231       0.038462      0.035179      0.052920      0.032458
20050131      -0.010137     -0.026556     -0.029278     -0.025290
20050228      -0.019651      0.022672      0.016636      0.018903
20050331       0.024432     -0.016935     -0.031835     -0.019118
20050429       0.003882     -0.025186     -0.046509     -0.020109
20050531       0.007735      0.037955      0.043808      0.029952
20050630      -0.044134      0.011534      0.032155     -0.000143
20050729      -0.004329      0.043327      0.058745      0.035968
20050831      -0.025797     -0.005946     -0.007217     -0.011222
20050930       0.008331      0.010565      0.010530      0.006949
20051031       0.007128     -0.020801     -0.033876     -0.017741
20051130       0.053377      0.040385      0.034319      0.035186
20051230      -0.011758      0.003455      0.013479     -0.000952
20060131      -0.065621      0.040033      0.076354      0.025467
20060228       0.011298     -0.001640      0.004836      0.000453
20060331       0.058108      0.019055      0.036979      0.011065
20060428      -0.005463      0.012962      0.009791      0.012187
20060531      -0.009540     -0.031048     -0.044332     -0.030917
20060630      -0.030648     -0.000408     -0.008479      0.000087
20060731      -0.008192     -0.001904     -0.022718      0.005086
20060831       0.041909      0.025061      0.025011      0.021274
20060929       0.043746      0.019424      0.009005      0.024566
20061031      -0.005382      0.037126      0.046211      0.031508
20061130       0.004842      0.023705      0.031168      0.016467
20061229       0.062642      0.010833      0.014793      0.012616
20070131      -0.031174      0.019428      0.022283      0.014059
20070228      -0.023856     -0.013957      0.002110     -0.021846
20070330       0.012890      0.012949      0.006543      0.009980
20070430       0.042421      0.039821      0.027044      0.043291
20070531       0.019533      0.038932      0.023112      0.032549
20070629       0.026078     -0.014756     -0.007929     -0.017816
20070731       0.012539     -0.031756     -0.043537     -0.031982
20070831       0.002838      0.011656     -0.011737      0.012864
20070928       0.072292      0.040860      0.025363      0.035794
20071031      -0.005797      0.025835      0.017406      0.014822
20071130      -0.069728     -0.049222     -0.076608     -0.044043
20071231      -0.023766     -0.004419     -0.010995     -0.008628
20080131      -0.046129     -0.062151     -0.045082     -0.061163
20080229      -0.054016     -0.021653     -0.021401     -0.034761
20080331       0.116777     -0.010480     -0.025314     -0.005960
20080430      -0.116455      0.051096      0.031907      0.047547
20080530      -0.060551      0.023838      0.031776      0.010674
20080630      -0.121094     -0.078449     -0.086631     -0.085962
20080731       0.059948     -0.013325     -0.001296     -0.009859
20080829      -0.006716      0.010572      0.013022      0.012191
20080930      -0.081495     -0.097996     -0.120109     -0.090791
20081031      -0.234902     -0.184587     -0.205222     -0.169425
20081128      -0.119939     -0.084613     -0.130320     -0.074849
20081231      -0.038439      0.022149      0.042154      0.007822
20090130      -0.251235     -0.077329     -0.024042     -0.085657
20090227      -0.272877     -0.100184     -0.107667     -0.109931
20090331       0.188014      0.086688      0.107429      0.085405
20090430       0.251236      0.109347      0.192760      0.093925
20090529       0.065613      0.067784      0.102314      0.053081
20090630      -0.123145     -0.003100      0.023910      0.000196
20090731       0.143345      0.081715      0.085217      0.074142
20090831       0.037313      0.031462      0.057209      0.033560
20090930       0.188489      0.045237      0.071233      0.035723
20091030      -0.131547     -0.028004     -0.050612     -0.019762
20091130       0.123422      0.057093      0.028444      0.057364
20091231      -0.049313      0.028413      0.054975      0.017771
20100129       0.062789     -0.037093     -0.011390     -0.036974
20100226       0.004975      0.034776      0.033603      0.028514
20100331       0.133250      0.063600      0.069240      0.058796
20100430       0.036264      0.020015      0.057837      0.014759
20100528      -0.133086     -0.079133     -0.076975     -0.081976
20100630      -0.111927     -0.050721     -0.056671     -0.053882
20100730       0.117892      0.071541      0.059994      0.068778
20100831      -0.101737     -0.042812     -0.047592     -0.047449
20100930       0.130525      0.091514      0.096348      0.087551
20101029      -0.014154      0.038534      0.040681      0.036856
20101130      -0.011860      0.005168      0.010661     -0.002290
20101231       0.164245      0.067131      0.068745      0.065300
20110131       0.101148      0.019155      0.014413      0.022646
20110228       0.045680      0.038158      0.037036      0.031957
20110331      -0.041587      0.003376      0.008576     -0.001047
20110429       0.019950      0.028683      0.019201      0.028495
20110531      -0.039609     -0.014934     -0.018550     -0.013501
20110630      -0.032077     -0.018391     -0.024111     -0.018258
20110729      -0.050371     -0.022448     -0.021813     -0.021474
20110831      -0.089336     -0.057470     -0.075715     -0.056791
20110930      -0.057633     -0.084872     -0.100947     -0.071762

Finding Derivatives:

Find y’ for

(A) y = 3e^x + 5 ln x

(B) y = x^4 – ln x^4

https://eazyweezyhomeworks.com/order/

Please help me solve these two questions.

Thank you (:

SPC CASE ANALYSIS: AMERICO DRILLING SUPPLIES

MGT 3332

On November 1, 2021, John Adams, a customer service representative of Americo Drilling Supplies (ADS), was summoned to the Houston office of Drilling Contractors, Inc. (DCI), to inspect three boxcars of mud-treating agents that ADS had shipped to the Houston firm. DCI had complained that the 25 Pound bags of treating agents received from ADS were light weighted.

The light-weight bags were initially detected by one of DCI’s receiving clerks, who noticed that the railroad side scale tickets indicated that the net weights were significantly less on all three of the boxcars than those of identical shipments received on October 25, 2021. ADS’s traffic department was called to determine if lighter-weight dunnage or pallets were used on the shipments. (This might explain the lighter weights.) ADS indicated, however, that no changes had been made in the loading or palletizing procedures. Hence, DCI randomly checked 25 of the bags and discovered that the average net weight was almost 24.5 pounds. Consequently, they concluded that the sample indicated a significance short-weight. ADS was then contacted, and Adams was sent to investigate the complaint and to issue credit to DCI.

DCI, however, was not completely satisfied with the issuance of credit for the short shipment. The charts followed by their mud engineers on the drilling platforms were based on 25-pound bags of treating agents. Lighter-weight bags might result in poor chemical control during the drilling operation and might adversely affect drilling efficiency. (Mud-treating agents are used to control the pH and other chemical properties of the open during drilling operations.) This could cause severe economic

consequences because of the extremely high cost of oil and natural gas drilling operations. Consequently, special use instructions had to accompany the delivery of these shipments to the drilling platforms. Moreover, the light-weight shipments had to be isolated in DCI warehouse, causing extra handling and poor space utilization. Hence, Adams was informed that CDI might seek a new supplier of mud-treating agents if in the future it received bags that deviated significantly below 25 pounds.

The quality control department at ADS suspected that the light-weight bags may have resulted from “growing pains” at the Orange, Texas plant. Because of the earlier energy crises, oil and natural gas exploration activity had greatly increased. This increased activity, in turn, created increased demand for products produced by related industries, including drilling muds. Consequently, ADS had to expand from one shift (6 A.M. to 2 P.M.) to a two-shift (2 P.M. to 10 P.M.) operation in Mid-2014, and finally to a three-shift operation (24 hours per day) in January of 2018.

The additional night shift bagging crew was staffed entirely by new employees. The most experienced foremen were temporarily assigned to supervise the night shift. Most emphasis was placed on increasing the output of bags to meet the ever-increasing demand. It was suspected that only occasional reminders were made to double-check the bag weight feeder. (A double check is performed by systematically weighting a bag on a scale to determine if the proper weight is being loaded by the weight-feeder. If there is significant deviation from 25 pounds, corrective adjustments are made to the weight-release mechanism.)

To verify this expectation, the quantity control staffs at ADS randomly sampled bags and prepared the following table (see Excel dataset). Note that four bags were sampled and weighted each hour (sample of size 4).

ANALYSIS

Assume you are John Adams of ADS.  Based on the following analysis, prepare a report to be submitted to both ADS and DCI executives regarding the status of the filling process at ADS and recommend method to improve quality control at the filling station and estimate the amount of credit to DCI.  Use the data provided in the Excel data file.

Insert all graphs and provide analysis in this word file after every question. Only The Word file is graded.

• Calculate the Range Column in Excel (Largest-Smallest) and find mean and standard deviations for Average Weight, Smallest, Largest, and Range columns.

• What is the standard deviation of individual bags if sample averages are based on 6 bags? Explain your finding. Hint: _x-bar = /sqrt(n). Having _x-bar based on part (a) calculation, solve for  given n= 4. So  = (_x-bar)*(sqrt(n))

• Construct a time series plot of all four variables (two graphs: one includes avg., smallest, and largest and the other has range data) and discuss your findings based on the graphs.

• Construct X-bar and R Charts, graph, and discuss your findings based on the control charts. Make sure to include the control limit calculations below. Is the process out of control?  Why? Explain.

• Is there any differences between performances of three shifts? Hint: (Carve out the morning, afternoon, and night shift data into three columns and graph their averages. Explain your findings based on graph.

• Use One Way Analysis of Variance (ANOVA) to compare the three groups (shifts) to test if there is significant differences in the performance of three shift averages. Use Alpha =0.01.  Indicate the Null and Alt. hypotheses and explain your findings based on ANOVA table.

• Assume Tolerance limits of 25±1.75 lbs. is specified in the sales contract and find the Process Capability index C_pk. Discuss if this process is capable to meet contractual agreement.

• Redo part g for all three shifts separately and determine their C_pk. Note that you must carve out the three shifts and find the mean and standard deviations for each shift separately and go through part b calculations for each shift to find  for each shift.

• If the process average is adjusted to 25.0 lbs. and process standard deviation (answer in part b) is reduced by 60%, what is the new C_pk? Are you comfortable for making such recommendation to management?

• Find the control limits for an X-bar and R chart if a new improved process has average of 25.0 lbs. and R-bar of 1.0 lbs. Assume n=5 for new process control. No graph needed.

• Estimate the amount of credit ($) must be given to DCI (for the past 36 months) if it purchased 30,000 bags per month at cost of $8 per lb.

• Provide complete conclusion regarding your findings and make recommendations regarding the filling process in your conclusion paragraph.

Grading Criteria 

Completeness/Correctness                              70%

Quality of Interpretations/Analysis                 20%

General Quality of Report/graphs/writing      10%

See Syllabus for Due Date