Statistics 401B
Fall 2014
Laboratory Assignment 2
The Places Rated Almanac uses nine rating criteria for rating cities in the U.S. The attached table lists
the rating values for Health Care and Environment criterion for 329 cities. The scores are computed using the
following component statistics : per capita physicians, teaching hospitals, medical schools, cardiac rehabilitation
centers, comprehensive cancer treatment centers, hospices, insurance/hospitalization costs index, flouridation of
drinking water, and air pollution. Answer question 1 through 8 using this data.
1. Use the JMP file places.jmp to perform a JMP distribution analysis of the Rating variable. This analysis
must contain the percentiles and the moments, a histogram, the box plot,and a stem-and-leaf diagram.
Turn in just one page of computer output for this part. In the rest of this lab, use the statistics computed
above as the known values of the corresponding parameters µ, σ 2 ,and M (Median) for this “population” .
2. Use the table of random numbers (Table 13, page 1122) in your textbook or the table attached, to draw a
random sample of size n = 12 from the above population. Enter the rating values in the selected sample
into a JMP data table and perform a JMP distribution analysis of the rating variable. This analysis must
contain the percentiles and the moments, a histogram, the box plot, and a stem-and-leaf diagram. Turn in
just one page of computer output for this part.
3. Using the method described in the attachment, use JMP to draw 3 random samples of size 12, 24, and 36,
respectively, in separate JMP data tables. For each sample, perform a JMP distribution analysis of the %
Higher Degrees variable to obtain the statistics needed to fill out the table below .
Statistic
n
Sample 1
Sample 2
Sample 3
ȳ
s2
s
R
Q(0.25)
Q(0.5)
Q(0.75)
IQR
4. For this exercise we shall define sampling error as the absolute difference between the sample statistic
(calculated from a sample) and the population parameter which it estimates. For example, ȳ is an estimate
of µ; thus the sampling error of ȳ is |ȳ − µ|.
(a) Compute the sampling error in the estimate ȳ of µ for each of the 3 samples.
(b) Compute the sampling error in the estimate s of σ for each of the 3 samples.
(c) Compute the sampling error in the sample median M for each of the 3 samples.
5. In each of the 3 JMP tables created in Problem #3, create an additional column labelled Sample containing
the sample number (1, 2 or, 3) as all its values. Change the Modeling Type of this variable to ordinal.
Combine these three JMP tables using Tables→Concatenate menu item into one JMP data table. Use
the Analyze→Fit Y by X to produce side-by-side box plots of the three samples as well as the normal
probability plots. Also compute the means, std. deviations, and std. errors of the mean, of the three
samples. Turn in just one page of computer output from this part.
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6. Assume that Y is a discrete random variable defined on the population of 329 elements given in the places
data table. Find the following probabilities.
P (Y = 731) =
P (806 < Y < 1690) =
P (Y < 731) =
P (806 ≤ Y ≤ 1690) =
P (Y ≥ 731) =
P (Y ≤ 900) =
P (Y = 581) =
P (Y > 1010) =
P (Y < 581) =
P (Y > 1950) =
P (Y ≥ 581) =
P (1050 ≤ Y ≤ 1150) =
7. A manufacturing firm purchases components for its products from suppliers. There have been quality
lapses in the switches supplied by a regular vendor. Suppose that, unknown to the firm, 6% of the switches
in each shipment by this vendor are defective. A quality engineer at the manufacturing firm selects a
random sample of 20 switches from a shipment from this vendor and inspects them to find whether there
are any defectives among them. Using the probability function of the Binomial distribution, calculate the
probability (round to 6 significant digits) that, in this sample
(a) no switch is found to be defective
(b) at most 4 are found to be defective
(c) exactly 5 are found to be defective
(d) more than 5 are found to be defective
You must show work. If 1000 switches are tested how many would you expect to be found defective?
Explain how you obtained your answer.
8.* A precision parts manufacturer produces heat-treated steel alloy bolts for use in rockets. The company
statistician obtains a random sample of 40 bolts from the weeks production lot and measures the length of
each to determine if they meet a preset standard.
(a) What is the target population?
(b) What is the variable of interest?
(c) Identify the sample.
(d) Is the variable of interest qualitative or quantitative?
(e) Describe a procedure you would use to select the random sample using a random digits table.
(f) What is the parameter of interest? (you may use a symbol and describe it in words)
(g) What is the estimate of the parameter you identified?
(h) Is it possible to obtain an estimate of the uncertainity of this estimate from the same data? How
would you compute this?
* This question relates to one of the primary objectives of this course as described in the syllabus. A similar
question will be included in the midterm/final exam to assess whether you have understood this concept.
Due Thursday, September 18, 2014 (turn-in by 2:20 p.m.)
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Place
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Rating
237
1656
618
1431
1853
640
621
965
432
669
2025
601
580
820
2508
598
833
1204
605
3195
637
1798
1203
782
420
3562
780
342
900
616
861
240
570
2661
479
441
1007
1692
804
731
815
453
5301
962
333
438
310
2550
975
916
Place
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
Rating
91
640
2465
994
1809
443
345
837
672
1463
708
999
1348
564
5766
243
2138
446
3167
721
1951
1421
833
1837
458
760
2825
2350
593
1113
2253
723
732
2533
1256
4142
593
640
1159
444
798
528
596
562
626
529
539
783
900
920
Place
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
Rating
872
594
655
724
607
818
731
1252
546
527
466
484
1060
1038
369
622
1731
1437
1364
43
1109
1274
667
706
916
1694
1260
818
1135
2087
2521
1006
1298
583
2467
875
685
2243
2437
679
1792
1181
740
700
1759
1152
731
1058
500
1043
Place
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
Rating
609
1711
1939
1067
398
960
596
686
655
548
314
1237
323
1111
1371
465
588
412
621
1202
477
759
1860
741
775
1861
509
1105
5153
2111
1083
900
732
593
2168
737
303
372
256
517
2043
2314
2589
884
97
3053
3934
1469
347
2482
3
Place
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
Rating
331
832
949
699
853
1850
3919
519
1245
2068
556
2586
7850
4106
507
1932
2530
2362
489
384
1623
338
2559
1574
765
812
1106
201
665
593
1117
563
1184
5158
1584
617
3413
694
834
1590
596
355
2467
198
468
931
3476
1154
274
615
Place
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
Rating
300
2448
2201
1036
2966
1969
969
1027
1022
603
223
2850
749
1232
352
1631
236
1337
2416
3726
2117
532
1035
1052
801
1084
1219
2715
700
593
394
1445
846
1041
830
497
1877
710
577
2610
612
505
342
1040
539
370
1189
453
343
1738
Place
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
Rating
1148
1372
1259
1581
674
672
391
1079
517
260
807
210
538
4361
1218
925
818
375
791
806
549
860
1445
1099
1805
317
713
1097
212
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