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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sample2 |
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sample3 |
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Last but not least, I want you to draw three random
samples of 20 students from the 1995 Witt New Student population, listed on the
back of this sheet, and record the proportion of students from
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proportion from |
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sample 1 |
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sample 2 |
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sample 3 |
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001 IN
002 OH
003 IN
004 IL
005 OH
006 OH
007 OH
008 IL
009 OH
010 OH
011 OH
012 OH
013 XX
014 OH
015 OH
016 OH
017 PA
018 OH
019 OH
020 IN
021 OH
022 IL
023 IN
024 OH
025 OH
026 OH
027 OH
028 OH
029 OH
030 XX
031 OH
032 NJ
033 OH
034 MA
035 MI
036 OH
037 OH
038 OH
039 KY
040 OH
041 TN
042 OH
043 IL
044 TX
045 OH
046 OH
047 OH
048 OH
049 OH
050 ME
051 OH
052 OH
053 OH
054 OH
055 NE
056 OH
057 OH
058 OH
059 OH
060 MI
061 OH
062 MD
063 OH
064 OH
065 KY
066 IL
067 OH
068 XX
069 OH
070 OH
071 OH
072 OH
073 OH
074 OH
075 OH
076 PA
077 CT
078 OH
079 OH
080 DE
081 OH
082 OH
083 IL
084 OH
085 MI
086 OH
087 MI
088 TN
089 OH
090 OH
091 MN
092 CT
093 OH
094 OH
095 MI
096 OH
097 XX
098 OH
099 OH
100 NC
101 OH
102 OH
103 CT
104 XX
105 OH
106 KY
107 OH
108 OH
109 OH
110 IL
111 IN
112 DC
113 OH
114 OH
115 OH
116 OH
117 OH
118 OH
119 UT
120 OH
121 MA
122 OK
123 OH
124 XX
125 OH
126 MD
127 IN
128 OH
129 OH
130 NJ
131 OH
132 OH
133 XX
134 IL
135 MI
136 NY
137 MI
138 OH
139 OH
140 OH
141 XX
142 OH
143 IL
144 OH
145 KY
146 VA
147 OH
148 OH
149 OH
150 OH
151 XX
152 OH
153 IL
154 MN
155 OH
156 OH
157 OH
158 OH
159 GA
160 SC
161 MN
162 OH
163 OH
164 OH
165 OH
166 PA
167 OH
168 OH
169 OH
170 OH
171 OH
172 OH
173 OH
174 OH
175 OH
176 OH
177 IL
178 OH
179 OH
180 OH
181 NC
182 OH
183 OH
184 FL
185 OH
186 OH
187 OH
188 OH
189 OH
190 OH
191 IN
192 OH
193 OH
194 OH
195 OH
196 OH
197 OH
198 OH
199 TN
200 CA
201 MI
202 OH
203 KY
204 IL
205 IN
206 OH
207 CT
208 OH
209 FL
210 OH
211 OH
212 IN
213 OH
214 OH
215 IL
216 XX
217 OH
218 OH
219 IN
220 OH
221 NY
222 PA
223 OH
224 MI
225 NY
226 MI
227 OH
228 IL
229 MO
230 PA
231 NY
232 OH
233 OH
234 OH
235 XX
236 FL
237 OH
238 OH
239 OH
240 OH
241 OH
242 XX
243 OH
244 OH
245 XX
246 NE
247 NY
248 MI
249 OH
250 OH
251 OH
252 OH
253 MA
254 OH
255 TN
256 OH
257 OH
258 OH
259 OH
260 AZ
261 OH
262 OH
263 MA
264 NJ
265 OH
266 OH
267 OH
268 OH
269 OH
270 MA
271 NY
272 OH
273 OH
274 OH
275 OH
276 IL
277 OH
278 OH
279 OH
280 OH
281 MD
282 OH
283 OH
284 OH
285 OH
286 MD
287 MI
288 OH
289 OH
290 OH
291 OH
292 OH
293 OH
294 OH
295 OH
296 OH
297 IL
298 IN
299 OH
300 IN
301 FL
302 PA
303 PA
304 OH
305 IL
306 IL
307 OH
308 OH
309 MD
310 OH
311 OH
312 MN
313 OH
314 IL
315 OH
316 OH
317 OH
318 IN
319 OH
320 OH
321 OH
322 IL
323 OH
324 PA
325 OH
326 PA
327 IN
328 OH
329 OH
330 MI
331 OH
332 NY
333 IL
334 NY
335 XX
336 GU
337 OH
338 CO
339 OH
340 OH
341 OH
342 IN
343 OH
344 OH
345 CO
346 XX
347 OH
348 OH
349 OH
350 MI
351 OH
352 OR
353 OH
354 OH
355 OH
356 OH
357 OH
358 OH
359 OH
360 OH
361 XX
362 OH
363 OH
364 XX
365 IN
366 OH
367 OH
368 XX
369 OH
371 OH
372 OH
373 OH
374 OH
375 OH
376 OH
377 OH
378 OH
379 OH
380 KY
381 IN
382 MA
383 OH
384 OH
385 OH
386 XX
387 IN
388 XX
389 OH
390 MI
391 KY
392 OH
393 OH
394 IN
395 OH
396 OH
397 OH
398 IN
399 OH
400 OH
401 KY
402 OH
403 IN
404 MI
405 IN
406 OH
407 OH
408 OH
409 PA
410 OH
411 OH
412 OH
413 OH
414 OH
415 OH
416 MI
417 OH
418 OH
419 NY
420 OH
421 OH
422 OH
423 OH
424 OH
425 OH
426 OH
427 OH
428 NC
429 IL
430 OH
431 CA
432 OH
433 OH
434 IN
435 MI
436 OH
437 OH
438 OH
439 OH
440 TN
441 OH
442 IN
443 MD
444 OH
445 NY
446 OH
447 PA
448 OH
449 KY
450 OH
451 OH
452 NY
453 OH
454 OH
455 OH
456 OH
457 NY
458 NY
459 OH
460 OH
461 OH
462 OH
463 FL
464 OH
465 OH
466 OH
467 IN
468 NY
469 OH
470 MI
471 XX
472 OH
473 XX
474 PA
475 OH
476 PA
477 OH
478 PA
479 NH
480 OH
481 MI
482 IN
483 KY
484 OH
485 MD
486 PA
487 OH
488 OH
489 OH
490 IN
491 OH
492 MI
493 OH
494 XX
495 OH
496 OH
497 MO
498 OH
499 OH
500 OH
501 OH
502 OH
503 OH
504 IN
505 MI
506 OH
507 XX
508 CO
509 OH
510 OH
511 OH
512 IL
513 OH
514 OH
515 OH
516 OH
517 NY
518 NY
519 OH
520 OH
521 IL
522 OH
523 OH
524 OH
525 OH
526 OH
527 OH
528 OH
529 OH
530 IN
531 OH
532 OH
533 OH
534 OH
535 OH
536 OH
537 OH
538 XX
539 WV
540 OH
541 MI
542 OH
543 OH
544 OH
545 OH
546 NY
547 OH
548 OH
549 TX
550 OH
551 WV
552 OH
553 MA
554 OH
555 OH
556 OH
557 IL
558 OH
559 OH
560 OH
561 OH
562 OH
563 OH
564 MA
565 OH
566 OH
567 OH
568 OH
569 NY
570 KY
571 OH
572 OH
573 OH
574 NY
575 PA
576 IL
577 OH
578 OH
579 IN
580 XX
581 PA
582 KY
583 DC
584 NH
585 OH
586 OH
587 XX
588 OH
589 IN
590 OH
591 OH
592 IN
593 OH
594 OH
595 MI
596 OH
597 OH
598 MI
599 OH
600 OH
601 OH
602 NY
603 OH
604 OH
605 OH
606 OH
607 OH
608 TX
609 OH
610 OH