It is very costly and time consuming to Import and Export. As part of an initial
ID: 3375239 • Letter: I
Question
It is very costly and time consuming to Import and Export. As part of an initial investigation exploring foreign markets entry into 10 different countries in four (4) global regions. The cost to EXPORT sea cargo in these countries is seen below:
Is there evidence, at 0.05 level of significance of a difference in the mean cost of EXPORTING across the global regions?
1. Compute the means on each group and the mean of means
2. Compute the sum of squares (SST)
3. Compute the sum of squares (SSA)
4. Compute the SSW
Country
Country
Region Cost to export (US$ per container) Cost to import (US$ per container) Cambodia East Asia & Pacific 755 900 China East Asia & Pacific 580 615 Hong Kong SAR, China East Asia & Pacific 575 565 Indonesia East Asia & Pacific 644 660 Malaysia East Asia & Pacific 435 420 Philippines East Asia & Pacific 585 660 Singapore East Asia & Pacific 456 439 Taiwan, China East Asia & Pacific 655 720 Thailand East Asia & Pacific 585 750 Vietnam East Asia & Pacific 610 600 Belarus Eastern Europe & Central Asia 1,510 2,315 Bulgaria Eastern Europe & Central Asia 1,551 1,626 Cyprus Eastern Europe & Central Asia 790 900 Lithuania Eastern Europe & Central Asia 825 980 Macedonia, FYR Eastern Europe & Central Asia 1,376 1,380 Montenegro Eastern Europe & Central Asia 855 915 Romania Eastern Europe & Central Asia 1,485 1,495 Russian Federation Eastern Europe & Central Asia 2,820 2,920 Turkey Eastern Europe & Central Asia 990 1,235 Ukraine Eastern Europe & Central Asia 1,865 2,155 Argentina Latin American & Carribbean 1,650 2,260 Belize Latin American & Carribbean 1,355 1,600 Brazil Latin American & Carribbean 2,215 2,275 Chile Latin American & Carribbean 980 965 Colombia Latin American & Carribbean 2,255 2,830 Costa Rica Latin American & Carribbean 1,030 1,020 Jamaica Latin American & Carribbean 1,500 1,560 Mexico Latin American & Carribbean 1,450 1,780 Peru Latin American & Carribbean 890 880 Venezuela, RB Latin American & Carribbean 2,590 2,868 Algeria Middle East & North Africa 1,260 1,330 Bahrain Middle East & North Africa 955 995 Egypt, Arab Rep. Middle East & North Africa 625 755 Iraq Middle East & North Africa 3,550 3,650 Jordan Middle East & North Africa 825 1,335 Kuwait Middle East & North Africa 1,085 1,242 Lebanon Middle East & North Africa 1,080 1,365 Qatar Middle East & North Africa 885 1,033 Saudi Arabia Middle East & North Africa 935 1,054 Syrian Arab Republic Middle East & North Africa 1,190 1,625Explanation / Answer
1. Compute the means on each group and the mean of means
Answer:
There are total four groups. The means of each group are summarised in the following tables:
East Asia & Pacific
Eastern Europe & Central Asia
Mean
588
1406.7
Standard Deviation
92.5455
618.4863
Count
10
10
Latin American & Caribbean
Middle East & North Africa
Mean
1591.5
1239
Standard Deviation
586.4254
832.6224
Count
10
10
Pooled StDev = 597.5
Grand Mean = Mean of means = (588+1406.7+1591.5+1239)/4 = 1206.3
2. Compute the sum of squares (SST)
Answer:
Formula for SST is given as below:
SST = ?(Xij – GM)2
Calculation table for SST is given as below:
No.
X1
X2
X3
X4
(X1 - GM)^2
(X2 - GM)^2
(X3 - GM)^2
(X4 - GM)^2
1
755
1510
1650
1260
203671.69
92233.69
196869.69
2883.69
2
580
1551
1355
955
392251.69
118818.09
22111.69
63151.69
3
575
790
2215
625
398539.69
173305.69
1017475.69
337909.69
4
644
825
980
3550
316181.29
145389.69
51211.69
5492929.69
5
435
1376
2255
825
594903.69
28798.09
1099771.69
145389.69
6
585
855
1030
1085
386013.69
123411.69
31081.69
14713.69
7
456
1485
1500
1080
562950.09
77673.69
86259.69
15951.69
8
655
2820
1450
885
303931.69
2604027.69
59389.69
103233.69
9
585
990
890
935
386013.69
46785.69
100045.69
73603.69
10
610
1865
2590
1190
355573.69
433885.69
1914625.69
265.69
Total
5880
14067
15915
12390
3900030.9
3844329.7
4578842.9
6250032.9
SST = 3900030.9 + 3844329.7+ 4578842.9 + 6250032.9
SST = 18573236
3. Compute the sum of squares (SSA)
Answer:
SSA = n*?(Xj – GM)2
SSA = 10*(588 - 1206.3)^2 + 10*(1406.7- 1206.3)^2 + 10*(1591.5- 1206.3)^2 + 10*(1239- 1206.3)^2
SSA = 5719034
4. Compute the SSW
SSW = SST – SSA
SSW = 18573236 - 5719034
SSW = 12854203
ANOVA table is given as below:
MS = SS/DF
F = MSA/MSW
One-way ANOVA: Cost to export (US$ per contain versus Region
Analysis of Variance for Cost to
Source DF SS MS F P
Region 3 5719034 1906345 5.34 0.004
Error 36 12854203 357061
Total 39 18573236
P-value = 0.004 < alpha value = 0.05
So, we reject the null hypothesis that there is no any significant difference in the average Cost to export for four global regions.
There is sufficient evidence to conclude that there is a significant difference in the average Cost to export for four global regions.
East Asia & Pacific
Eastern Europe & Central Asia
Mean
588
1406.7
Standard Deviation
92.5455
618.4863
Count
10
10
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