MONTE CARLE ON STATA SOFTWARE Case Solution
Appendix
Results of Tests before Simulation
Two Sample Mean Comparison test
. ttest MilesperGallonforUSCars == MilesPerGallonforJapaneseCa, unpaired
Two-sample t test with equal variances
——————————————————————————
Variable |    Obs       Mean   Std. Err.  Std. Dev.  [95% Conf. Interval]
———+——————————————————————–
Milesp~s |Â Â Â Â Â 80Â Â Â Â Â 15.975Â Â Â .4689657Â Â Â 4.194556Â Â Â 15.04155Â Â Â 16.90845
MilesP~a |Â Â Â Â Â 80Â Â Â Â 30.4625Â Â Â .6755082Â Â Â 6.041929Â Â Â 29.11793Â Â Â 31.80707
———+——————————————————————–
combined |Â Â Â Â 160Â Â Â 23.21875Â Â Â .7056974Â Â Â 8.926444Â Â Â Â Â 21.825Â Â Â Â 24.6125
———+——————————————————————–
diff |Â Â Â Â Â Â Â Â Â Â Â -14.4875Â Â Â .8223382Â Â Â Â Â Â Â Â Â Â Â Â Â Â -16.11169Â Â -12.86331
——————————————————————————
diff = mean(MilesperGallon~s) – mean(MilesPerGallon~a)Â Â Â Â Â Â Â t = -17.6174
Ho: diff = 0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â degrees of freedom =Â Â Â Â Â 158
Ha: diff < 0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Ha: diff != 0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Ha: diff > 0
Pr(T < t) = 0.0000Â Â Â Â Â Â Â Â Pr(|T| > |t|) = 0.0000Â Â Â Â Â Â Â Â Â Pr(T > t) = 1.0000
Mann-Whitney Test
. ranksum MilesPerGallon, by(GroupingVariableCars)
Two-sample Wilcoxon rank-sum (Mann-Whitney) test
GroupingVa~s |     obs   rank sum   expected
————-+———————————
0 |Â Â Â Â Â Â 37Â Â Â Â Â Â Â 1530Â Â Â Â Â 1498.5
1 |Â Â Â Â Â Â 43Â Â Â Â Â Â Â 1710Â Â Â Â Â 1741.5
————-+———————————
combined |Â Â Â Â Â Â 80Â Â Â Â Â Â Â 3240Â Â Â Â Â Â Â 3240
unadjusted variance   10739.25
adjustment for ties     -37.64
———-
adjusted variance     10701.61
Ho: MilesP~n(Groupi~s==0) = MilesP~n(Groupi~s==1)
z =Â Â 0.304
Prob > |z| =Â Â 0.7607
Results of Tests after Simulation
Two Sample Mean Comparison Test
. ttest MilesPerGallon == SimulatedrMilesPerGallon, unpaired
Two-sample t test with equal variances
——————————————————————————
Variable |     Obs       Mean   Std. Err.  Std. Dev.  [95% Conf. Interval]
———+——————————————————————–
MilesP~n |Â Â Â Â Â 80Â Â Â 23.21875Â Â Â .3903345Â Â Â 3.491258Â Â Â 22.44181Â Â Â 23.99569
Simula~n |Â Â Â Â Â 80Â Â Â Â 22.0625Â Â Â .3455613Â Â Â 3.090794Â Â Â 21.37468Â Â Â 22.75032
———+——————————————————————–
combined |Â Â Â Â 160Â Â Â 22.64063Â Â Â .2638525Â Â Â Â Â 3.3375Â Â Â 22.11952Â Â Â 23.16173
———+——————————————————————–
diff |Â Â Â Â Â Â Â Â Â Â Â Â 1.15625Â Â Â .5213191Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â .1265967Â Â Â 2.185903
——————————————————————————
diff = mean(MilesPerGallon) – mean(SimulatedrMile~n)Â Â Â Â Â Â Â Â Â t =Â Â 2.2179
Ho: diff = 0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â degrees of freedom =Â Â Â Â Â 158
Ha: diff < 0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Ha: diff != 0Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Ha: diff > 0
Pr(T < t) = 0.9860Â Â Â Â Â Â Â Â Pr(|T| > |t|) = 0.0280Â Â Â Â Â Â Â Â Â Pr(T > t) = 0.0140
Mann-Whitney Test
. ranksum SimulatedrMilesPerGallon, by(GroupingVariableCars)
Two-sample Wilcoxon rank-sum (Mann-Whitney) test
GroupingVa~s |     obs   rank sum   expected
————-+———————————
0 |Â Â Â Â Â Â 37Â Â Â Â Â 1615.5Â Â Â Â Â 1498.5
1 |Â Â Â Â Â Â 43 Â Â Â Â Â 1624.5Â Â Â Â Â 1741.5
————-+———————————
combined |Â Â Â Â Â Â 80Â Â Â Â Â Â Â 3240Â Â Â Â Â Â Â 3240
unadjusted variance   10739.25
adjustment for ties    -114.16
———-
adjusted variance     10625.09
Ho: Simula~n(Groupi~s==0) = Simula~n(Groupi~s==1)
z =Â Â 1.135
Prob > |z| =Â Â 0.2563…………….
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