Generating Random Phenomena Name:
_______________
OK, guys, here’s one of the most tedious exercises
of the semester: I need you all to replicate the following random phenomena,
and to give me your results by class next time, so that I can consolidate
everyone’s results in time for my presentation next time. This is also an assignment on which I need
lots of data, so please do this individually (i.e., not in pairs).
1) Roll a die
four times, and record the individual rolls below. Then calculate the mean of these four rolls,
and record that mean. Please don’t
round off these means. Repeat this
for a total of 3 samples.
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roll 1 |
roll 2 |
roll 3 |
roll 4 |
mean roll |
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sample 1 |
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sample 2 |
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sample 3 |
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Next time we’ll look at the distribution of all the
means. To that end, please give me your
three sample means from these samples of 4 rolls each.
2) Repeat the
above procedure, but this time with 3 samples of 10 dice each.
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r 1 |
r 2 |
r 3 |
r 4 |
r 5 |
r 6 |
r 7 |
r 8 |
r 9 |
r10 |
mean roll |
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sample 1 |
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sample 2 |
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sample 3 |
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Once again, I need your three sample means from
these samples of 10 rolls each.
3) On the
other side of this sheet is a list of the SAT math scores for all 398 New
Students who entered Witt in 1995 (who reported SAT scores as part of the
admission process). I’ve labeled them
with three-digit identification labels for your convenience. Guess what – I’d like you to use the random number
table to generate three simple random samples of 25 students each, then calculate
and report the sample mean SAT math score for each of your three samples. (I won’t bother leaving room for the 25
scores in each sample, since all the scores are on the other side, and I don’t
need the individual scores anyway.)
Round off to the 0.1’s digit (i.e., 538.8).
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mean SAT score |
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sample 1 |
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sample 2 |
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sample 3 |
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That’s all.
Please remember the deadline, so that I can compile the results.
ID sat
ID sat ID
sat ID sat
ID sat ID
sat ID sat
ID sat
-------- --------
-------- -------- --------
-------- -------- --------
001
570 051
500 101 590
151 470 201
650 251 590
301 360 351
590
002
690 052
750 102 650
152 630 202
630 252 550 302 390
352 640
003
660 053
440 103 500
153 660 203
660 253 530
303 570 353
610
004
610 054
630 104 440
154 640 204
720 254 620
304 470 354
530
005
440 055
660 105 670
155 530 205
700 255 530
305 600 355
710
006
620 056
350 106 660
156 740 206
660 256 600
306 410 356
500
007
690 057
540 107 660
157 660 207
390 257 600
307 490 357
710
008
500 058
470 108 510
158 620 208
400 258 530
308 570 358
580
009
660 059
590 109 670
159 640 209
680 259 680
309 470 359
520
010
310 060
520 110 590
160 670 210
470 260 640
310 660 360
650
011
630 061
540 111 530
161 610 211
650 261 540
311 530 361
400
012
590 062
460 112 520
162 470 212
510 262 750
312 580 362
500
013
520 063
390 113 680
163 530 213
470 263 490
313 630 363
430
014
490 064
440 114 700
164 430 214
640 264 470
314 650 364
480
015
530 065
530 115 680
165 620 215
580 265 520
315 680 365
510
016
570 066
550 116 460
166 530 216
610 266 570
316 610 366
390
017
540 067
460 117 540
167 480 217
540 267 530
317 620 367
600
018
450 068
750 118 410
168 620 218
460 268 460
318 570 368
410
019
520 069
650 119 370
169 690 219
610 269 440
319 690 369
600
020
530 070
710 120 450
170 620 220
580 270 510
320 690 370 370
021
540 071
500 121 500
171 710 221
700 271 660
321 700 371
450
022 380 072
580 122 710
172 660 222
640 272 410
322 440 372
780
023
740 073
580 123 680
173 510 223
750 273 590
323 570 373
540
024
430 074
390 124 420
174 470 224
530 274 480
324 580 374
460
025
510 075
480 125 590
175 580 225
720 275 590
325 550 375
650
026
560 076
530 126 690
176 360 226
430 276 660
326 710 376
660
027
520 077
660 127 720
177 490 227
610 277 570
327 560 377
370
028
530 078
470 128 620
178 620 228
400 278 580
328 680 378
600
029
560 079
450 129 470
179 730 229
570 279 550
329 720 379
660
030
470 080
490 130 620
180 540 230
660 280 370
330 580 380
470
031
440 081
630 131 490
181 540 231
420 281 570
331 480 381
770
032
560 082
640 132 650
182 420 232
480 282 460
332 430 382
580
033
530 083
420 133 430
183 630 233
640 283 490
333 670 383
650
034
620 084
440 134 540
184 530 234
500 284 570
334 450 384
530
035
530 085
420 135 520
185 470 235
600 285 510
335 330 385
460
036
380 086
440 136 620
186 550 236
660 286 610
336 450 386
600
037
430 087
430 137 670
187 420 237
370 287 620
337 550 387
620
038
580 088
570 138 680
188 670 238 620
288 440 338
510 388 510
039
630 089
430 139 480
189 450 239
560 289 520
339 570 389
490
040
470 090
440 140 390
190 590 240
710 290 580
340 460 390
670
041
540 091
700 141 520
191 460 241
710 291 700
341 330 391
400
042
460 092
540 142 680
192 690 242
440 292 430
342 570 392
480
043
400 093
380 143 640
193 560 243
550 293 590
343 660 393
620
044
490 094
570 144 610
194 620 244
560 294 430
344 660 394
650
045
550 095
460 145 510
195 520 245
470 295 640
345 440 395
540
046
600 096
530 146 710
196 550 246
660 296 620
346 590 396
500
047
390 097
630 147 500
197 500 247
360 297 560
347 410 397
350
048
660 098
520 148 440
198 390 248
580 298 680
348 660 398
610
049
700 099
470 149 560
199 680 249 670 299
650 349 420
050
610 100
460 150 720
200 660 250
500 300 350 350 670
Distribution of the Sample
Proportion Name: __________
Remember the worksheet for which you rolled
dice? The point of the worksheet was to
examine the sampling distribution of the sample mean. That’s why I had you generate several samples
(of dice rolls) and calculate the sample mean for each sample – so we could see
how these sample means vary. Now I want
to do the same thing for a different statistic: the sample proportion. So I want you to generate several samples (of
coin spins this time), and calculate the sample proportion (of heads) in each
sample – so we can see how these sample proportions vary. Get ready for more tedium!
First, I want to make sure you understand the
spinning process. You must give the
penny lots of rotational momentum, and it must come to rest without hitting
anything. The former requires that you
don’t just give the coin a little twist with your wrist, but that you hold the
penny on edge with one finger and flick it with your other finger – as if
place-kicking a football, sort of. The
latter requires a large, flat, hard surface.
If the penny hits anything before coming to rest, disregard that
attempt.
Believe it or not, pennies spun in this fashion are
not equally likely to land heads up and tails up. I’ll explain why after we collect the
data. Please use a penny from the
1960’s; 1961 and 1962 are ideal to bring out this effect. Record the year of the penny that you use:
______
For now, I’d like you to generate three samples of
10 spins each, and three samples of 20 spins each. Then calculate the proportion of heads in
each of those samples. (The sample
proportions should be multiples of 0.1 in the samples of 10, and multiples of
0.05 in the samples of 20.)
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spin: |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
prop. of H’s |
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sample 1 |
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sample 2 |
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sample 3 |
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spin: |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
prop. H’s |
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sample1 |
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