Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
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Chapter 9.3, Problem 17E
a.
To determine
Construct an ANOVA table and the find the
b.
To determine
Check whether there is a difference in the measured weights among the operators using the ANOVA table. Find the value of test statistics and P-value if so and explain the reason if not.
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Cheek teeth of extinct primates. The characteristics of cheek teeth (e.g., molars) can provide anthropologists with information on the dietary habits of extinct mammals. The cheek teeth of an extinct primate species were the subject of research reported in the American Journal of Physical Anthropology (Vol. 142, 2010). A total of 18 cheek teeth extracted from skulls discovered in western Wyoming were analyzed. Researchers recorded the dentary depth of molars (in millimeters) for a sample of 18 cheek teeth extracted from skulls. These depth measurements are listed in the accompanying table. Anthropologists know that the mean dentary depth of molars in an extinct primate species— called Species A—is 15 millimeters. Is there evidence to indicate that the sample of 18 cheek teeth come from some other extinct primate species (i.e., some species other than Species A)?
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Each of three operators made two weighings of several silicon wafers. Results are presented
in the following table for three of the wafers. All the wafers had weights very close to 54 g.
so the weights are reported in units of ug above 54 g. (Based on the article "Revelation of a
Microbalance Warmup Effect," J. Buckner, B. Chin, et al., Statistical Case Studies for
Industrial Process Improvement, SIAM-ASA, 1997:39 45.)
Operator 1
Operator 2
15
10
Operator 3
14
Wafer
11
10
2
210
208
205
201 208
207
111
113
102
105 108
111
Construct an ANOVA table. You may give ranges for the P-values.
b. Can it be determined from the ANOVA table whether there is a difference in the
measured weights among the operators? If so, provide the value of the test statistic and
the P-value. If not, explain why not.
3.
The authors of the paper "Statistical Methods for Assessing Agreement Between Two Methods of Clinical Measurement"† compared two different instruments for measuring a person's ability to breathe out air. (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen people participated in the study, and for each person air flow was measured once using the Wright meter and once using the mini-Wright meter.
Subject
Mini-WrightMeter
WrightMeter
Subject
Mini-WrightMeter
WrightMeter
1
512
494
10
445
433
2
430
395
11
432
417
3
520
516
12
626
656
4
428
434
13
260
267
5
500
476
14
477
478
6
600
557
15
259
178
7
364
413
16
350
423
8
380
442
17
451
427
9
658
650
(a)
Suppose that the Wright meter is considered to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. If the two types of meters produce different…
Chapter 9 Solutions
Statistics for Engineers and Scientists
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