S01 MANAGERIAL STATISTICS

MODULE 11- SOCRATES AND ERASMUS

GROUP 3
Christian Willson Aca-ac
Jane Jowaher Caoile
Marion Fidelis De Leon
Minette Gabriel

Male

Signs U null Statement

Ho: = 0.5 Ho: M = 0.5

Ha: ≠ 0.5 Ha: M ≠ 0.5

M 16
F 18

Let
u=the proportion of male students enrolled in Erasmus program for
academic year 2005-2006
population proportion
testing ≠
p - null 0.5
n 34
part 16
p - hat 0.4705882353
z -0.34299717
p-value 0.731600589

one tailed two tailed: if Ha "="

alpha z-value z-value (>) Decision Decision: p-value
0.01 -2.326347874 2.575829306 Do not reject Ho Do not reject Ho
0.001 -3.090232305 3.290526728 Do not reject Ho Do not reject Ho
0.05 -1.644853625 1.959963986 Do not reject Ho Do not reject Ho
0.1 -1.281551564 1.644853625 Do not reject Ho Do not reject Ho

Since we do not reject Ho (at alpha .01, .001, .05,.1), the proportion of g
 Since we do not reject Ho (at alpha .01, .001, .05,.1),
the proportion of gender in Erasmus program is balance.

Female

Signs U null Statement

Ho: = 0.5 Ho: M = 0.5

Ha: ≠ 0.5 Ha: M ≠ 0.5

M 16
F 18

Let
u=the proportion of female students enrolled in Erasmus program for
academic year 2005-2006
 population proportion
testing ≠
p - null 0.5
n 34
part 18
p - hat 0.5294117647
z 0.3429971703
p-value 1.268399411

one tailed two tailed: if Ha "="

alpha z-value z-value (>) Decision
0.01 -2.326347874 2.575829306 Do not reject Ho
0.001 -3.090232305 3.290526728 Do not reject Ho
0.05 -1.644853625 1.959963986 Do not reject Ho
0.1 -1.281551564 1.644853625 Do not reject Ho

1, .001, .05,.1), the proportion of gender in Erasmus program is balance.

 Table 1 Students by field of study 2003-2004 according to home country
Subject AT BE BG CY CZ DK EE

.05,.1), Agricultur
37 156 51 0 187 18 6
s balance. al sciences

Architectu
re, 128 163 32 0 168 54 12
Planning
Art and
193 209 42 0 182 60 47
design
Business
1,117 1,089 97 7 584 364 47
studies
Education,
Teacher 260 414 12 24 228 74 2
training
Engineerin
g,
248 384 133 3 481 112 22
Technolog
y

Geography
32 28 12 0 90 27 9
, Geology

Humanitie
147 105 14 0 148 141 9
s

Languages
,
505 603 73 15 464 346 51
Philologic
al sciences

Mathemati
Law 231 357 37 0 185 103 28
cs,
146 139 86 0 123 20 4
Informatic
Medical
ssciences 144 349 60 12 222 115 12
Natural
143 51 33 0 113 33 4
sciences
Social
Communi 250 500 48 3 309 171 32
sciences
cation and
112 212 19 0 14 44 12
informatio
Other
nareas
science 28 30 2 0 91 4 8
Total 3,721 4,789 751 64 3,589 1,686 305
 Table 2 Erasmus students 2003-2007 by home country and host country
Home
Code AT BE BG CY CZ DK
Country
Austria AT 79 3 5 51 104
Belgium BE 105 11 1 51 84
Bulgaria BG 52 46 14
Cyprus CY 1 0 0 2
Czech
CZ 211 134 103
Republic
Denmark DK 70 44 2 19
Estonia EE 16 10 19
Finland FI 229 148 5 9 126 37
Decision: p-value France FR 361 420 9 10 206 500
Do not reject Ho Germany DE 387 330 17 7 207 410
Do not reject Ho Greece GR 71 140 6 8 63 45
Do not reject Ho Hungary HU 110 98 44
Do not reject Ho Iceland IS 10 4 54
Ireland IE 35 47 6 1 26 30
Italy IT 339 633 8 7 86 357
Latvia LV 8 27 13
Liechtenst
LI 0 0 2
ein
Lithuania LT 49 70 145
Luxembou
LU 17 1 0 0 2 2
rg
Malta MT 4 5 0 0 0 2
Netherland
NL 98 184 1 0 44 158
s
Norway NO 50 28 0 0 0 53
Poland PL 159 358 362
Portugal PT 53 250 8 8 103 63
Romania RO 38 163 29
Slovakia SK 44 50 11
Slovenia SI 59 30 19
Spain ES 298 1,054 11 0 169 573
Sweden SE 142 42 0 0 38 25
United
UK 143 117 5 4 107 136
Kingdom
EUI* EUR 2
Total 3,161 4,513 90 62 1,298 3,396
*European University Institute, Florence
 FI FR DE GR HU IS IE IT LV LI LT

64 398 181 81 136 3 3 317 14 0 48

30 519 762 149 75 0 30 877 9 9 37

326 651 906 143 114 24 90 756 31 0 63

1,383 6,573 5,023 306 450 56 593 1,963 88 10 241

100 320 535 81 126 22 24 267 27 0 56

487 2,833 1,376 143 147 20 52 1,545 10 0 189

33 259 433 46 66 3 12 206 14 0 25

136 598 1,048 131 64 13 51 1,144 13 0 33

316 3,321 3,528 327 248 47 305 3,346 21 0 92

117 1,449 1,474 191 159 7 142 1,455 7 0 87

108 570 803 104 64 4 45 392 13 0 65
291 399 1,021 172 125 4 46 1,045 8 0 85
93 843 879 87 29 3 62 453 6 0 43
307 1,787 2,067 343 200 15 210 2,220 38 0 97
100 295 425 38 23 0 32 723 5 0 17
60 166 227 43 32 0 8 120 4 0 16
3,951 20,981 20,688 2,385 2,058 221 1,705 16,829 308 19 1,194
EE FI FR DE GR HU IS IE IT LV LI
7 227 528 262 30 30 15 132 461 5 1
5 218 768 306 75 28 3 121 467 4 0
16 136 227 62 6 39
14 9 4 13 0 3
241 510 931 78 43 180
2 5 260 302 13 3 12 36 111
47 42 59 6 2 26
35 413 654 72 162 14 111 190 9
21 727 2,804 218 169 23 1,081 1,550 3
25 918 3,997 165 171 47 926 1,755 23 8
1 116 420 356 20 2 27 248 1
201 276 566 42 15 227
1 26 40 3 2 16
2 40 557 292 12 5 109
28 367 2,859 1,994 180 129 29 230 4 1
42 18 111 2 2 9
3 1 1
180 77 294 18 10 67
0 1 27 39 0 0 0 9 0 0
0 6 3 6 0 6 52
7 275 543 391 42 49 11 88 256 6 0
0 15 156 190 15 0 0 17 85 0 0
310 855 1,870 122 74 481
3 95 325 295 53 59 4 19 713 5 1
33 1,125 457 87 21 448
52 80 191 24 2 58
24 62 125 6 1 56
12 501 3,412 2,553 178 67 21 513 4,250 1 0
10 24 484 426 17 28 9 80 137 3 0
8 233 2,303 1,127 60 31 9 21 740 1 0
4 1
166 4,932 20,275 16,874 1,593 951 199 3,587 12,743 65 11
LU MT NL NO PL PT RO SK SI ES SE

0 0 80 27 112 69 61 37 23 566 19

4 2 109 19 321 264 64 18 24 854 64

4 3 145 69 232 205 87 34 38 905 90

15 6 1,089 275 1,342 386 290 169 146 3,244 902

43 11 354 92 126 215 47 15 17 602 69

6 9 224 112 752 479 604 106 35 3,109 424

8 2 84 5 158 66 147 10 6 450 31

2 1 81 39 171 60 116 22 12 654 48

14 7 253 84 675 334 451 84 97 2,568 121

6 31 303 77 429 190 98 25 51 1,413 195

0 1 55 35 301 87 176 23 3 674 46
8 32 219 142 247 407 209 71 6 1,211 176
7 4 51 22 361 216 206 29 2 1,062 84
19 5 992 137 928 487 355 29 65 1,701 313
1 5 264 10 68 155 54 3 19 800 56
1 0 85 11 53 162 40 7 2 221 29
138 119 4,388 1,156 6,276 3,782 3,005 682 546 20,034 2,667
LT LU MT NL NO PL PT RO SK SI ES
12 0 14 215 82 22 60 8 6 16 631
7 3 13 377 40 69 207 30 10 9 1,287
23 34 43
2 3
203 189 286
3 4 117 27 12 15 5 5 259
10 4 30
15 16 377 15 60 58 13 22 29 479
25 6 43 891 246 314 288 167 30 40 5,115
49 1 28 862 463 395 283 27 26 24 4,325
1 1 5 106 17 14 90 3 0 2 374
145 42 125
13 1 36
4 5 110 8 10 18 3 291
28 71 607 156 174 766 129 29 20 5,688
24 4 9
4 2
30 51 61
0 0 0 0 1 6 0 0 0 14
7 2 3
10 0 18 140 21 93 14 3 5 907
0 0 78 0 36 0 0 0 231
294 222 546
26 0 4 250 38 125 68 7 14 920
72 119 285
3 29 30 59
25 30 63
24 0 9 1,263 200 176 992 59 32 22
11 0 11 236 22 24 25 3 0 6 370
3 0 12 365 69 42 97 10 16 6 1,636

218 14 253 6,733 1,523 1,459 3,766 536 181 201 24,076
UK EUI Total Table 3 Sample of Erasmus student enrollments for the academic
Family First Home
23 0 2,717 Study area
name name country

96 0 4,893 Algard Erik Norway Business studies

489 0 6,138 Alinei Gratian Romania Business studies

Birgitte Engineering,
1,332 0 29,187 Andersen Denmark
Brix Technology

163 0 4,326 Bay Hilde Norway Social sciences

Bednarczy
269 0 14,314 Tomasz Poland Law
k

Engineering,
88 0 2,350 Berberich Remi Germany
Technology

206 8 5,215 Berculo Ruwan Netherlands Business studies

Dorothe Geography,
2,875 0 21,171 Engler Germany
a Geology

754 1 9,602 Ernst Folker Germany Business studies

Education,
92 0 4,179 Fouche Elie France Communication
Teacher training
232 0 7,070 Garcia Miguel Spain and information
220 0 5,139 Guenin Aurelie France science
Humanities
Johanness Sanne
585 1 14,214 Denmark Business studies
Languages,
en Lyng
83 0 3,589 Justnes Petter Norway Philological
Ane sciences
32 0 1,482 Kauffeldt Denmark Business studies
Katrine United Mathematics,
7,539 10 135,586 Keddie Nikki
Jan Kingdom Informatics
Lorenz Sebastia Germany Business studies
Guillau
n
Mallet France Business studies
me
 Margher
Manzo Italy Business studies
Marginean ita Agricultural
SE UK Total Florin Romania
u
Miechowk Anne sciences
Engineering,
305 410 3,721 France
a Sophie Technology
149 341 4,789 Mynborg Astrid Denmark Humanities
Architecture,
9 44 751 Napolitano Silvia Italy
United Planning
5 8 64 Neilson Alison Business studies
Kingdom Education,
163 317 3,589 Ou Kalvin France
Teacher training
Engineering,
30 330 1,686 Rachbauer Thomas Austria
Technology
Mathematics,
26 8 305 Savreux Margaux France
Czech Informatics
Agricultural
101 552 3,951 Seda Jiri
Semorado Republic
Czech sciences
1,062 4,652 20,981 Petra Natural sciences
va Maria Republic
1,653 3,159 20,688 Torres Spain Humanities
Teresa
109 139 2,385 Ungerstedt Malin Sweden Law
Languages,
Alexand
58 109 2,058 Ververken Belgium Philological
er
Alessand
2 13 221 Viscardi Italy sciences
Business studies
ra
Katarzyn
57 37 1,705 Zawisza Poland Business studies
a
399 1,511 16,829
32 7 308
1 5 19
120 22 1,194
3 16 138
1 22 119
389 635 4,388
42 159 1,156
286 337 6,276
95 178 3,782
42 86 3,005
17 32 682
17 29 546
670 2,974 20,034
494 2,667
238 7,539
1 2 10
6,082 16,628 135,586
ollments for the academic year 2005-2006

Gender

M
M
M
F
F
M
F
F
M
M
F
M
F
F
F
F
M
M
F
M
F
F
F
M
F
F
S01 MANAGERIAL STATISTICS
MODULE 12- PAR INC.
GROUP 3
Christian Willson Aca-ac
Jane Jowaher Caoile
Marion Fidelis De Leon
Minette Gabriel

Model Sample size

Current New Mean
264 277 Standard dev.
261 269 Confidence coeff.
267 263 Level of sig.
272 266 Z value
258 262 Standard error
283 251 Margin of error
258 262 Pt. est of diff
266 289 Lower limit
259 286 Upper limit
270 264
270 272
287 259 We are 95% confident that the difference between the mean driving d
289 264 is -1.32 and 6.87 yards.
280 280
272 274
275 281 Also, using analysis of variance..
265 276
260 269 Let
278 268
275 262
263 274 Ho:
264 266 Ha:
284 262
263 271 Anova: Single Factor
260 260
283 281 SUMMARY
255 250 Groups
272 263 Current
266 278 New
268 264
281 283
274 250 ANOVA
273 253 Source of Variation
263 260 Between Groups
275 270 Within Groups
267 263
279 261 Total
274 255
276 263 Let:
262 279 p
alpha
n

Decision
 Current
40
270.28
8.7529848388846
0.95
0.05
1.95996398454005
2.08903962108466
4.09444241960313
2.77
(1.32)
6.87

t that the difference between the mean driving distances of the current and new Par Inc. balls

u1 = mean of current model

u2 = mean of new model
u1=u2
u1≠u2

Count
40
40

SS
154.0125
6807.975

6961.9875

2
0.05
80
Do not reject Ho.

From the above result, since F value(1.76454452315115) is not greater than F critical value (3.96347192060052), we do
not reject Ho. Therefore, the means are equal of current and new golf balls. The mean difference between the mean
distances for the two models could not be attributed to a difference in the two models.
Sample size

New
40
267.50
9.896904463
Sum Average Variance
10811 270.275 76.61474359
10700 267.5 97.948717949

df MS F P-value F crit
1 154.0125 1.7645445232 0.1879322849 3.9634719206
78 87.281730769

79
S01 MANAGERIAL STATISTICS
MODULE 12- AIR FORCE TRAINING PROGRAM
GROUP 3
Christian WilLson Aca-ac
Jane Jowaher Caoile
Marion Fidelis De Leon
Minette Gabriel

Course Completion Times (hours) Course Completion Times

(hours) for Proposed
for Current Training Method Computer-Assisted Method

76 74
78 74
76 73
79 77
77 76
69 76
76 75
75 77
78 77
82 78
79 75
79 76
77 77
80 69
72 69
65 78
76 73
66 74 1
74 78
79 76
82 77
77 76 2
78 77
70 72
76 74
72 75
72 75 3
79 75
76 77
74 78
74 80
69 72
73 76
73 76
76 77
72 71
74 73
79 75
71 74
76 76
73 79
77 73
72 72
70 77
81 75 4
77 75
72 78
70 76
77 75
69 76
84 75
78 76 5
70 72
78 78
75 80
74 72
73 76
81 77
73 72
75 77
74 82
 Current Training Method Computer-Assisted Method

Mean 75.0655737705 Mean 75.4262295082

Standard Error 0.50509364628 Standard Error 0.32090975222
Median 76 Median 76
Mode 76 Mode 76
Standard Deviation 3.94490748712 Standard Deviation 2.50638528824
Sample Variance 15.562295082 Sample Variance 6.28196721311
Kurtosis -0.0693252764 Kurtosis 0.58694041387
Skewness -0.2205335581 Skewness -0.2874862429
Range 19 Range 13
Minimum 65 Minimum 69
Maximum 84 Maximum 82
Sum 4579 Sum 4601
Count 61 Count 61
Confidence Level(95.0%) 1.01033772056 Confidence Level(95.0%) 0.64191507842

Same Median and mode and slight difference with its mean.
It implies that in both methods, the central value of sample data is 76.
Further, range of current training method is higher at 19 showing that it is widely dispersed compared to Computer assisted of 13.

Difference bet. means -0.3606557377

Means are nearly the same meaning completion time of students are comparable.

Computer-assisted method lower at 2.5 compared to current at 3.9 which indicates that computer assisted has less variations.

F test Two sample variance (0.01)

Current Training Method Computer-Assisted Method
Mean 75.0655737705 75.4262295081967
Variance 15.562295082 6.28196721311475
Observations 61 61
df 60 60
F 2.477296451
P(F<=f) one tail 0.000289016
F critical one-tail 1.836259361

As a value of F (2.477) is greater than Fcritical (1.83), Null Hypothesis (Ho) is rejected.
We canconclude that the two methods differ in terms of variance.
The data shows that the Computer – Assisted Method has the smaller variance indicating that students trained
under thismethod are more consistent in terms of completion

There is no significant difference in the means of two methods.

There is a significant difference in the variance of two methods.
The Computer Assited is prefered with significantly lower variance.
Under this method, there should be less chance of faster students waiting for slower
students to complete the training.

It is necessary to test also the qualititive learning experience of the students not just based on time finished.
Computer assisted of 13.

d has less variations.