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 Ohio in each of
your three samples. (Be sure to use
three-digit numbers in your randomization.)
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proportion from Ohio |
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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