Statistics 401D
Spring 2016
Laboratory Assignment 2
The County and City Data Book is the most comprehensive source of information about the individual
counties and cities in the United States. It includes data for all U.S. states, counties, and cities with a population
of 25,000 or more. The attached table lists the percentage of people with graduate or professional degrees in 249
selected cities extracted from the 2007 data book and is one of the education related measurements. A 3-digit
city number has been assigned to each data value so that we can tag each observation uniquely for the pupose
of selecting random samples. Answer question 1 through 5 using this data.
1. Use the JMP file education.jmp to perform a JMP distribution analysis of the % Higher Degrees variable.
This analysis must contain the percentiles and the moments, a histogram, the box plot,and a stem-andleaf 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 values of the % Higher Degrees
variable in the selected sample into a JMP data table and perform a JMP distribution analysis of the %
Higher Degrees 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.
Tabulate the above statistics in a suitable manner as part of your solution.
1
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.
Provide written answers to the following problems showing work.
6. Suppose that a machine making electrical resistors is observed over a period of time. It is found that 10% of
all resistors produced by the machine have resistant values that fall outside the target range and therefore
are considered defective. Twenty resistors are randomly tested from a certain production run. Calculate
the probability (round to 4 significant digits) that in this sample
(a)
(b)
(c)
(d)
(e)
no resistor is found to be defective
at most 4 are found to be defective
exactly 5 are found to be defective
Five or more are found to be defective
all 20 are found to be defective
If 1000 resistors are tested how many would you expect to be found defective?
7. The background radiation rate as measured at a certain location with a particular Geiger counter is known
to be 1800 counts per hour. We will use s Poisson distribution to model the radiation counts in a specified
time interval.
(a) If the Geiger counter is run at the location for a 10 second interval, how many counts would you
expect to observe?
(b) What is the uncertainty associated with the number of counts observed in 10 seconds?
(c) At this location, calculate the probability of observing
i.
ii.
iii.
iv.
0 counts in 10 seconds
no more than 3 counts in 10 seconds
at least 4 counts in 10 seconds
exactly 8 counts in 20 seconds
Note: You must use the Poisson pmf for your calculations and show all your work. Your may check your
answers using Table 15 of the text book or using a Poisson calculator available on the internet.
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)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
What is the target population?
What is the variable of interest?
Identify the sample.
Is the variable of interest qualitative or quantitative?
Describe a procedure you would use to select the random sample using a random digits table.
What is the parameter of interest? (you may use a symbol and describe it in words)
What is the estimate of the parameter you identified?
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 Tuesday, February 2nd, 2016 (turn-in by 10:20 a.m.
2
during lab)
City
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
% Higher
Degrees
7.6
15.0
10.3
14.1
12.6
12.2
13.3
6.5
7.6
9.0
7.9
19.1
14.9
10.6
15.5
6.3
7.6
35.5
8.8
7.8
9.5
6.4
10.9
5.9
4.5
2.3
5.4
3.3
22.3
5.9
12.0
5.7
11.9
5.7
13.7
4.4
26.9
3.7
8.5
9.7
6.6
5.0
3.0
13.6
8.0
3.0
10.0
3.7
4.6
22.8
City
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
% Higher
Degrees
3.5
8.9
8.0
9.4
2.7
4.0
11.7
16.1
18.9
12.9
4.2
18.3
9.0
11.1
9.9
4.5
24.3
19.6
14.9
3.7
5.4
10.5
7.1
18.3
13.4
15.4
19.5
11.9
5.8
8.5
4.1
5.4
18.5
17.5
6.3
25.2
25.2
6.4
8.3
10.2
11.5
22.3
3.3
8.6
7.5
7.7
2.6
7.4
10.9
6.8
City
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
% Higher
Degrees
8.5
21.4
10.8
20.3
17.1
7.2
9.9
7.7
12.4
11.2
10.6
12.1
7.5
24.3
12.9
6.4
11.9
6.1
6.7
4.4
9.1
9.6
7.3
7.7
4.2
19.0
8.8
8.6
7.8
17.1
9.9
7.1
12.9
10.8
13.3
7.5
11.0
18.1
43.8
8.5
7.8
9.5
44.4
4.7
4.3
9.5
7.3
12.7
8.4
5.5
3
City
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
% Higher
Degrees
15.2
14.8
9.9
4.6
10.9
9.7
7.9
11.8
9.9
9.0
6.5
3.3
9.5
9.8
3.3
8.9
3.9
1.9
10.9
14.7
13.4
8.7
13.1
8.9
11.4
10.3
11.4
20.2
8.9
11.0
16.7
11.1
7.3
11.5
4.7
10.6
5.0
5.8
8.7
9.4
17.7
14.2
9.7
5.8
7.0
9.4
15.1
11.5
16.9
9.1
City
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
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
% Higher
Degrees
9.1
5.8
10.7
8.0
11.9
8.0
6.8
8.1
15.6
9.4
4.0
8.2
7.6
10.0
6.3
8.1
5.2
6.2
10.5
9.3
5.3
10.2
8.7
6.6
3.8
19.0
8.8
8.8
6.3
13.8
13.6
2.4
28.2
35.9
10.7
8.6
8.1
8.5
5.3
13.4
10.4
22.5
20.5
9.7
7.6
8.0
5.7
21.0
6.9