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Part 3 Inferential Statistics
QNT/561 Version 9
Part 3: Inferential Statistics
Option 1: Manufacturing Database
1. The National Association of Manufacturers (NAM) contracts with your consulting company to
determine the estimate of mean number of production workers. Construct a 95% confidence interval
for the population mean number of production workers. What is the point estimate? How much is the
margin of error in the estimate?
2. Suppose the average number of employees per industry group in the manufacturing database is
believed to be less than 150 (1000s). Test this belief as the alternative hypothesis by using the 140
SIC Code industries given in the database as the sample. Let α = .10. Assume that the number of
employees per industry group are normally distributed in the population.
3. You are also required to determine whether there is a significant difference between mean Value
Added by the Manufacturer and the mean Cost of Materials in manufacturing using alpha of 0.01.
4. You are requested to determine whether there is a significantly greater variance among values of
Cost of Materials than of End-of-Year Inventories.
Option 2: Hospital Database
1. As a consultant, you need to use the Hospital database and construct a 90% confidence interval to
estimate the average census for hospitals. Change the level of confidence to 99%. What happened to
the interval? Did the point estimate change?
2. Determine the sample proportion of the Hospital database under the variable “service” that are
“general medical” (category 1). From this statistic, construct a 95% confidence interval to estimate the
population proportion of hospitals that are “general medical.” What is the point estimate? How much
error is there in the interval?
3. Suppose you want to “prove” that the average hospital in the United States averages more than 700
births per year. Use the hospital database as your sample and test this hypothesis. Let alpha be 0.01.
4. On average, do hospitals in the United States employ fewer than 900 personnel? Use the hospital
database as your sample and an alpha of 0.10 to test this figure as the alternative hypothesis.
Assume that the number of births and number of employees in the hospitals are normally distributed
in the population.
Option 3: Consumer Food
1. Suppose you want to test to determine if the average annual food spending for a household in the
Midwest region of the U.S. is more than \$8,000. Use the Midwest region data and a 1% level of
significance to test this hypothesis. Assume that annual food spending is normally distributed in the
population.
2. Test to determine if there is a significant difference between households in a metro area and
households outside metro areas in annual food spending. Let α = 0.01.
3. The Consumer Food database contains data on Annual Food Spending, Annual Household Income,
and Non-Mortgage Household Debt broken down by Region and Location. Using Region as an
independent variable with four classification levels (four regions of the U.S.), perform three different
one-way ANOVA’s—one for each of the three dependent variables (Annual Food Spending, Annual
1
Part 3 Inferential Statistics
QNT/561 Version 9
Household Income, Non-Mortgage Household Debt). Did you find any significant differences by
region?
Option 4: Financial Database
1. Use this database as a sample and estimate the earnings per share for all corporations from these
data. Select several levels of confidence and compare the results.
2. Are the average earnings per share for companies in the stock market less than \$2.50? Use the
sample of companies represented by this database to test that hypothesis. Let α = .05.
3. Test to determine whether the average return on equity for all companies is equal to 21. Use this
database as the sample and α = .10. Assume that the earnings per share and return on equity are
normally distributed in the population.
4. Do various financial indicators differ significantly according to type of company? Use a one-way
ANOVA and the financial database to answer this question. Let Type of Company be the independent
variable with seven levels (Apparel, Chemical, Electric Power, Grocery, Healthcare Products,
Insurance, and Petroleum). Compute three one-way ANOVAs, one for each of the following
dependent variables: Earnings Per Share, Dividends Per Share, and Average P/E Ratio.
2
Week 6 Options
QNT/561 Version 9
University of Phoenix Material
Option 1: Manufacturing Database
This database contains six variables taken from 20 industries and 140 subindustries in the United States.
Some of the industries are food products, textile mill products, furniture, chemicals, rubber products,
primary metals, industrial machinery, and transportation equipment. The six variables are Number of
Employees, Number of Production Workers, Value Added by Manufacture, Cost of Materials, End-of-Year
Inventories, and Industry Group. Two variables, Number of Employees and Number of Production
Workers, are in units of 1000. Three variables, Value Added by Manufacture, Cost of Materials, and Endof-Year Inventories, are in million-dollar units. The Industry Group variable consists of numbers from 1 to
20 to denote the industry group to which the particular subindustry belongs.
Option 2: Hospital Database
This database contains observations for six variables on U.S. hospitals. These variables include
Geographic Region, Control, Service, Census, Number of Births, and Personnel.
The region variable is coded from 1 to 7, and the numbers represent the following regions:
1 = South
2 = Northeast
3 = Midwest
4 = Southwest
5 = Rocky Mountain
6 = California
7 = Northwest
Control is a type of ownership. Four categories of control are included in the database:
1 = government, nonfederal
2 = nongovernment, not-for-profit
3 = for-profit
4 = federal government
Service is the type of hospital. The two types of hospitals used in this database are:
1 = general medical
2 = psychiatric
Option 3: Consumer Food
The consumer food database contains five variables: Annual Food Spending per Household, Annual
Household Income, Non-Mortgage Household Debt, Geographic Region of the U.S. of the Household,
and Household Location. There are 200 entries for each variable in this database representing 200
different households from various regions and locations in the United States. Annual Food Spending per
Household, Annual Household Income, and Non-Mortgage Household Debt are all given in dollars. The
variable Region tells in which one of four regions the household resides. In this variable, the Northeast is
coded as 1, the Midwest is coded 2, the South is coded as 3, and the West is coded as 4. The variable
Location is coded as 1 if the household is in a metropolitan area and 2 if the household is outside a metro
area. The data in this database were randomly derived and developed based on actual national norms.
Option 4: Financial Database
1
Week 6 Options
QNT/561 Version 9
The financial database contains observations on seven variables for 100 companies. The variables are
Type of Industry, Total Revenues (\$ millions), Total Assets (\$ millions), Return on Equity (%), Earnings
per Share (\$), Dividends per Share (\$), and Average Price per Earnings (P/E) ratio. The companies
represent seven different types of industries. The variable Type displays a company’s industry type as:
1 = apparel
2 = chemical
3 = electric power
4 = grocery
5 = healthcare products
6 = insurance
7 = petroleum
2
SIC Code No. Emp. No. Prod. Wkrs. Value Added by Mfg.
Cost of Materials End Yr. Inven.
201
433
370
23518
78713
3630
202
131
83
15724
42774
3157
203
204
169
24506
27222
8732
204
100
70
21667
37040
3407
205
220
137
20712
12030
1155
206
89
69
12640
13674
3613
207
26
18
4258
19130
1946
208
143
72
35210
33521
7199
209
171
126
20548
19612
3135
211
21
15
23442
5557
5506
212
3
2
287
163
42
213
2
2
1508
314
155
214
6
4
624
2622
554
221
52
47
2471
4219
929
222
74
63
4307
5357
1427
223
13
12
673
1061
325
224
17
13
817
707
267
225
169
147
8986
10421
2083
226
51
41
3145
4140
697
227
55
44
4076
7125
1446
228
84
76
3806
8994
1014
229
61
47
4276
5504
1291
231
27
22
1239
716
356
232
200
178
9423
8926
2314
233
294
250
11045
11121
2727
234
38
32
1916
2283
682
235
17
14
599
364
197
236
34
28
2063
1813
450
237
1
1
34
71
17
238
31
25
1445
1321
526
239
224
179
10603
12376
2747
241
83
68
5775
9661
578
242
172
147
10404
19285
3979
243
257
209
13274
18632
3329
244
51
43
1909
2170
355
245
82
68
4606
7290
580
249
94
78
5518
8135
1604
251
273
233
12464
12980
3535
252
70
53
5447
4011
829
253
37
29
2290
5101
447
254
81
61
4182
3755
956
259
54
39
2818
2694
718
261
15
11
2201
3279
725
262
116
90
18848
20596
4257
263
55
42
9655
10604
1502
265
212
163
15668
24634
3976
267
271
272
273
274
275
276
277
278
279
281
282
283
284
285
286
287
289
291
295
299
301
302
305
306
308
311
313
314
315
316
317
319
321
322
323
324
325
326
327
328
329
331
332
333
334
335
232
403
121
136
69
604
41
21
65
55
80
115
213
126
51
126
37
76
67
25
14
65
8
61
122
763
15
3
37
2
6
8
7
12
60
64
17
31
45
205
17
72
221
128
35
15
162
182
136
16
57
25
437
28
12
50
39
45
79
106
75
28
75
24
45
43
18
8
54
7
46
95
598
12
2
31
2
4
7
6
9
51
50
13
25
36
152
13
53
174
106
26
11
123
25918
30692
17982
17857
9699
38407
3878
3989
4388
4055
16567
25025
59813
31801
8497
28886
12277
11547
26006
3464
2187
7079
442
4528
7275
55621
1313
162
1907
53
747
328
233
1717
6532
4850
3509
2176
2696
15739
999
7838
29180
9061
4200
1410
16670
28963
8483
6940
8863
2823
29572
3811
1047
2055
1098
11298
34596
27187
19932
9849
46935
11130
13085
132880
6182
4446
7091
496
3805
7195
57264
1865
163
1682
85
395
255
177
943
3527
4254
2282
1387
1183
17010
565
5432
45696
6913
11184
5735
31892
5427
894
1216
3736
874
4300
688
577
504
236
2644
6192
11533
4535
2178
8577
2354
2749
10718
658
670
1067
175
1057
1411
11874
404
35
716
62
199
75
40
282
1505
883
828
700
600
1966
263
1652
12198
1543
1834
694
6377
336
339
341
342
343
344
345
346
347
348
349
351
352
353
354
355
356
357
358
359
361
362
363
364
365
366
367
369
371
372
373
374
375
376
379
381
382
384
385
386
387
391
393
394
395
396
399
94
32
33
140
45
432
104
259
129
40
300
79
94
205
295
192
265
259
201
392
74
171
108
157
49
258
588
151
772
377
141
31
18
81
47
186
272
268
27
61
6
43
13
103
35
24
179
79
23
27
107
32
315
81
211
99
24
219
55
70
133
211
110
172
96
147
293
51
120
87
117
37
120
368
106
634
190
108
23
14
29
35
68
141
157
17
36
4
30
10
76
26
19
123
5856
3164
3999
11750
4412
27974
6936
19880
7793
3528
21718
10513
9545
18178
22673
19221
23110
41135
17521
25322
6700
14278
9466
13428
3459
38705
84059
13920
105899
45220
7903
2590
1435
9986
3564
21071
29028
31051
2390
14032
415
2761
685
8327
2643
1406
11199
4696
2790
9364
8720
3527
31527
4909
21531
6232
1689
19273
12954
11858
23474
14343
16515
18543
60857
21819
13897
5523
12657
12578
11065
7621
29591
44486
13398
223639
42367
7760
4363
1674
8120
5476
8760
18028
16787
1020
8114
382
3646
506
6604
1789
997
8530
938
800
1453
3124
1121
7204
1768
3997
1181
1077
6460
3679
3339
7344
6730
6823
7898
10277
4857
4964
1495
3887
2299
3076
1070
9467
13145
3514
15852
36814
2165
1233
412
4770
1102
6183
7681
7761
426
2290
177
1451
328
2608
799
415
2861
Indus. Grp.
1
1
1
1
1
1
1
1
1
2
2
2
2
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
7
7
7
7
7
8
8
8
8
8
8
8
8
8
9
9
9
9
9
9
9
9
10
10
10
11
11
11
11
11
12
12
12
12
12
12
12
13
13
13
13
13
13
13
13
13
14
14
14
14
14
14
14
15
15
15
15
15
15
15
15
15
16
16
16
16
16
16
16
16
16
17
17
17
17
17
17
17
17
18
18
18
18
18
18
18
19
19
19
19
19
19
20
20
20
20
20
20
Hospital Geog. Region Control Service Census Births Personnel
1
1
2
1
107
312
792
2
1
1
1
198 1077
1762
3
1
2
1
356 1027
2310
4
1
1
1
100
355
328
5
7
1
1
9
168
181
6
4
2
1
159 3810
1077
7
4
4
1
65
735
742
8
4
2
1
48
1
131
9
1
2
1
253 1733
1594
10
1
1
1
21
257
233
11
1
1
1
27
169
241
12
6
3
1
30
430
203
13
6
3
1
43
0
325
14
6
2
1
233 2049
676
15
6
4
1
2
211
347
16
6
1
1
11
16
79
17
6
3
1
84 2648
505
18
6
2
1
219 2450
1543
19
6
3
1
112 1465
755
20
6
3
1
124
0
959
21
6
3
1
50 1993
325
22
6
2
1
142 2275
954
23
6
2
1
111 1494
1091
24
6
1
1
140 1313
671
25
6
3
1
28
451
300
26
6
2
1
154 1689
753
27
6
2
1
150 1583
607
28
6
3
1
144 2017
929
29
6
3
1
42
995
354
30
6
2
1
77 2045
408
31
5
2
1
119 1686
1251
32
5
2
1
27
503
386
33
5
2
1
15
126
144
34
2
2
1
179 2026
2047
35
2
2
1
175 1412
1343
36
2
2
1
461 1517
1723
37
1
3
2
32
0
96
38
1
2
1
74
0
529
39
1
1
1
414 2719
3694
40
1
2
1
253 1074
1042
41
1
3
1
180 1421
1071
42
1
1
1
184
762
1525
43
1
2
1
243 3194
1983
44
1
2
1
115
496
670
45
1
1
1
215 1442
1653
46
1
3
2
48
0
167
47
48
49
50
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
1
1
1
1
1
1
1
1
7
7
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
1
1
1
1
1
1
1
1
2
3
2
1
1
3
2
1
2
2
3
1
3
2
2
2
2
2
3
2
2
2
4
2
2
1
3
1
2
2
2
1
2
2
1
3
1
1
3
4
1
2
3
3
2
1
3
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
124
189
181
9
28
288
108
154
76
165
295
101
69
12
185
378
114
49
106
460
43
29
125
17
10
14
173
207
223
82
64
139
109
298
52
34
168
21
390
47
80
50
113
45
76
129
60
1107
2989
113
0
0
173
1064
759
1317
1751
0
0
714
99
2243
3966
1308
0
2514
3714
126
556
1327
415
216
339
1217
2641
790
520
35
1168
793
0
0
14
0
0
0
0
776
451
0
145
1284
1
319
793
841
316
93
373
263
943
605
596
1165
568
507
479
136
1456
3486
885
243
1001
3301
337
1193
1161
322
185
205
1224
1704
815
712
156
1769
875
790
308
70
494
111
1618
244
525
472
94
297
847
234
401
94
95
96
97
98
99
100
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
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
3
1
1
1
3
3
3
3
3
5
5
5
5
3
3
3
5
5
5
2
2
2
2
2
2
5
5
5
2
2
2
2
2
2
1
2
4
2
1
3
3
4
1
3
2
1
2
2
3
1
1
1
4
3
1
4
2
1
4
2
3
1
2
3
3
1
4
3
3
2
2
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
418
17
138
64
62
131
265
456
40
310
72
19
112
375
15
78
123
54
96
82
1106
30
56
36
127
180
59
127
37
13
100
47
194
172
516
120
179
140
78
68
186
91
340
254
108
61
174
2154
295
496
589
806
701
3968
0
0
3655
0
0
0
0
0
3063
169
66
827
570
0
0
0
342
494
0
0
0
0
286
235
339
398
1275
5699
1364
714
0
0
0
779
0
2202
3346
1071
352
254
3928
198
1231
545
663
820
2581
1298
126
2534
251
85
432
864
66
556
347
239
973
439
1849
102
262
885
549
611
330
1471
75
262
328
377
575
1916
2620
571
703
535
160
202
1330
370
3123
2745
815
576
502
141
142
143
144
145
146
147
148
149
150
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
2
2
2
2
2
1
1
1
1
1
3
3
3
3
3
3
3
3
3
3
7
7
7
7
7
2
2
2
2
2
1
1
1
3
3
1
1
1
1
1
1
1
1
1
5
5
5
1
3
2
2
1
2
1
4
1
2
2
2
4
1
2
2
1
3
4
1
2
1
1
4
2
1
4
2
2
2
4
3
3
4
2
2
3
3
2
3
4
3
3
3
3
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
306
28
395
923
335
46
316
416
74
86
38
147
232
138
38
245
171
51
28
797
56
69
40
163
231
523
31
43
66
231
11
144
43
185
82
49
24
63
274
93
86
28
25
181
39
302
80
0
0
699
2462
3311
0
4207
0
339
130
91
1143
0
0
509
1026
0
447
1161
0
922
562
78
0
2122
0
0
0
710
1165
466
1106
376
0
637
0
352
447
1227
963
3038
0
0
868
1189
2849
1728
808
50
728
4087
3012
68
3090
1358
576
284
145
2312
1124
336
415
1779
338
453
437
261
609
647
61
2074
2232
948
409
153
741
1625
538
789
395
956
362
144
229
396
2256
731
1477
102
106
939
392
3516
785
188
189
190
191
192
193
194
195
196
197
198
199
200
5
2
2
1
1
1
7
7
7
7
5
5
5
2
2
2
1
2
3
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
63
31
170
203
296
83
84
29
187
77
104
85
47
2171
364
0
2993
0
1964
601
387
1946
545
0
838
51
607
273
630
1379
1108
583
514
216
1593
1055
399
834
104
Region: 1 Location:
Annual
Annual
Non
= NE 2 = 1 = Metro
Food
Househol mortgage MW 3 =
2=
Spending d Income household S
4 = Outside
(\$)
(\$)
debt (\$)
W
Metro
8909
56697
23180
1
1
5684
35945
7052
1
1
10706
52687
16149
1
1
14112
74041
21839
1
1
13855
63182
18866
1
1
15619
79064
21899
1
1
2694
25981
8774
1
1
9127
57424
15766
1
1
13514
72045
27685
1
1
6314
38046
8545
1
1
7622
52408
28057
1
1
4322
41405
6998
1
1
3805
29684
4806
1
1
6674
49246
13592
1
1
7347
41491
4088
1
1
2911
26703
15876
1
1
8026
48753
16714
1
1
8567
55555
16783
1
1
10345
71483
21407
1
1
8694
50980
19114
1
1
8821
46403
7817
1
1
8678
51927
14415
1
1
14331
84769
17295
1
1
9619
59062
16687
1
1
9286
57952
14161
1
1
8206
58355
19538
1
1
16408
81694
15187
1
1
12757
69522
14651
1
1
17740
96132
0
1
1
7739
57796
22057
1
1
15383
88276
1896
1
1
4579
32264
7979
1
1
11679
65928
0
1
1
12877
69924
27330
1
1
16232
91108
9876
1
1
9621
54070
19908
1
1
8171
47238
17819
1
1
12128
77427
31340
1
1
8642
59805
4963
1
1
12400
60334
6632
1
1
9185
54114
18593
1
2
7862
9775
6771
3059
13211
7408
11581
14233
3352
2630
9093
12652
9559
6112
10431
12630
4578
9551
10262
9551
10143
8955
10197
11234
9320
9089
12300
11484
11215
7204
5579
11723
9353
7761
4261
9830
12386
8673
10944
9910
9928
4264
7971
8290
12669
7272
9784
40680
58263
52008
39643
70309
46450
76140
80833
31899
21647
65924
65923
62811
42335
65134
64621
36553
62910
70727
57634
56549
59662
57350
56447
61136
51526
79979
66733
75359
40795
39128
75482
63998
45845
38223
66787
77852
55825
57022
64263
75881
34343
41243
53021
66991
49719
58399
15202
1486
21713
12179
13221
5602
33874
11478
2762
2663
11355
5132
12613
3149
15196
21433
5502
11376
13287
11857
16136
11627
18432
10871
0
4902
17270
15145
15611
8975
6576
12508
0
6671
8576
1178
936
14167
9018
12768
17423
21323
21009
20151
9250
20838
16065
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
9187
5866
9456
6270
9518
10968
8865
9226
4913
6976
8152
2887
8062
8895
8444
6148
4563
8185
3391
7436
9522
11290
10403
4693
5626
11869
13055
8783
13031
3681
5549
4108
6314
7700
7479
9093
9863
8043
9552
9286
7987
3875
10746
6888
5479
6949
10650
50477
39112
51886
34797
62348
78704
53620
51577
34761
60968
51281
25013
59238
47344
52645
35309
34355
50630
29056
48721
50459
72805
56954
39343
38833
55021
77605
57937
63343
36479
40381
26309
41421
54579
40551
50369
54422
51836
73600
51873
48003
36519
75152
44974
48923
43769
75947
9407
20409
11668
146
5201
17002
32004
15922
17704
17799
8167
18763
10815
11814
22469
17139
10612
21187
15735
18363
16478
21238
22218
24696
14371
35576
817
18591
25531
17950
14257
26581
22470
29065
31757
6404
24334
26213
36374
29631
17261
13579
10659
23711
4594
21221
33357
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
1
1
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
5188
5311
4691
8056
11304
8112
8696
5869
3776
11829
13087
10986
5762
11617
9895
16293
8185
13972
11243
4635
10063
8426
7436
11747
15397
6842
9678
12852
10114
8496
6689
15696
9841
12529
10210
8868
6426
11096
10086
2587
12492
8456
6801
6339
7802
9717
6026
41423
40189
36772
59690
53654
59067
65962
37254
33568
56934
88822
59635
38407
78627
47710
64443
58871
87954
54778
39825
49536
60102
49139
51052
70500
54894
60570
57625
56956
61400
50532
72774
69981
66891
67431
64782
38987
64867
50421
27076
51784
54135
53291
49804
52205
72841
46238
33641
17791
5829
19594
23066
240
0
10157
14143
0
17565
27863
18867
11894
22930
31687
35424
11549
12552
19494
12195
13787
22356
4553
12025
16217
4106
31228
25907
1093
17106
17793
21607
17689
19995
14489
17864
5839
8689
17534
20284
22037
23342
34943
28579
22349
20165
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4