Problem

Cheek teeth of extinct primates. Refer to the American Journal of Physical Anthropology (V...

Cheek teeth of extinct primates. Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) study of the characteristics of cheek teeth (e.g., molars) in an extinct primate species, Exercise. Recall that the researchers measured the dentary depth of molars (in millimeters) for 18 cheek teeth extracted from skulls. These depth measurements are reproduced in the next table and saved in the CHEEKTEETH file. The researchers are interested in the median molar depth of all cheek teeth from this extinct primate species. In particular, they want to know if the population median differs from 15 mm.

a. Specify the null and alternative hypotheses of interest of the researchers.
b. Explain why the sign test is appropriate to apply in this case.

18.12
19.48
19.36
15.94
15.83
19.70
15.76
17.00
16.20
13.96
16.55
15.70
17.83
13.25
16.12
18.13
14.02
14.04

z
.00
.01
.02
.03
.04
.05
.06
.07
.08
.09
.0
.0000
.0040
.0080
.0120
.0160
.0199
.0239
.0279
.0319
.0359
.1
.0398
.0438
.0478
.0517
.0557
.0596
.0636
.0675
.0714
.0753
.2
.0793
.0832
.0871
.0910
.0948
.0987
.1026
.1064
.1103
.1141
.3
.1179
.1217
.1255
.1293
.1331
.1368
.1406
.1443
.1480
.1517
.4
.1554
.1591
.1628
.1664
.1700
.1736
.1772
.1808
.1844
.1879
.5
.1915
.1950
.1985
.2019
.2054
.2088
.2123
.2157
.2190
.2224
.6
.2257
.2291
.2324
.2357
.2389
.2422
.2454
.2486
.2517
.2549
.7
.2580
.2611
.2642
.2673
.2704
.2734
.2764
.2794
.2823
.2852
.8
.2881
.2910
.2939
.2967
.2995
.3023
.3051
.3078
.3106
.3133
.9
.3159
.3186
.3212
.3238
.3264
.3289
.3315
.3340
.3365
.3389
1.0
.3413
.3438
.3461
.3485
.3508
.3531
.3554
.3577
.3599
.3621
1.1
.3643
.3665
.3686
.3708
.3729
.3749
.3770
.3790
.3810
.3830
1.2
.3849
.3869
.3888
.3907
.3925
.3944
.3962
.3980
.3997
.4015
1.3
.4032
.4049
.4066
.4082
.4099
.4115
.4131
.4147
.4162
.4177
1.4
.4192
.4207
.4222
.4236
.4251
.4265
.4279
.4292
.4306
.4319
1.5
.4332
.4345
.4357
.4370
.4382
.4394
.4406
.4418
.4429
.4441
1.6
.4452
.4463
.4474
.4484
.4495
.4505
.4515
.4525
.4535
.4545
1.7
.4554
.4564
.4573
.4582
.4591
.4599
.4608
.4616
.4625
.4633
1.8
.4641
.4649
.4656
.4664
.4671
.4678
.4686
.4693
.4699
.4706
1.9
.4713
.4719
.4726
.4732
.4738
.4744
.4750
.4756
.4761
.4767
2.0
.4772
.4778
.4783
.4788
.4793
.4798
.4803
.4808
.4812
.4817
2.1
.4821
.4826
.4830
.4834
.4838
.4842
.4846
.4850
.4854
.4857
2.2
.4861
.4864
.4868
.4871
.4875
.4878
.4881
.4884
.4887
.4890
2.3
.4893
.4896
.4898
.4901
.4904
.4906
.4909
.4911
.4913
.4916
2.4
.4918
.4920
.4922
.4925
.4927
.4929
.4931
.4932
.4934
.4936
2.5
.4938
.4940
.4941
.4943
.4945
.4946
.4948
.4949
.4951
.4952
2.6
.4953
.4955
.4956
.4957
.4959
.4960
.4961
.4962
.4963
.4964
2.7
.4965
.4966
.4967
.4968
.4969
.4970
.4971
.4972
.4973
.4974
2.8
.4974
.4975
.4976
.4977
.4977
.4978
.4979
.4979
.4980
.4981
2.9
.4981
.4982
.4982
.4983
.4984
.4984
.4985
.4985
.4986
.4986
3.0
.4987
.4987
.4987
.4988
.4988
.4989
.4989
.4989
.4990
.4990
c. A MINITAB printout of the analysis is shown below. Locate the test statistic on the printout.
d. Find the p -value on the printout, and use it to draw a conclusion. Test using α =.05.

Cheek teeth of extinct primates. Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) study of the characteristics of cheek teeth (e.g., molars) in an extinct primate species, Exercise. In addition to degree of wear, the researchers recorded the dentary depth of molars (in millimeters) for 18 cheek teeth extracted from skulls. These depth measurements are listed in the accompanying table and saved in the CHEEKTEETH file. Summarize the data graphically with a stem-and-leaf display. Is there a particular molar depth that occurs more frequently in the sample?

Data on Dentary	Depth (mm) of Molars
18.12	16.55
19.48	15.70
19.36	17.83
15.94	13.25
15.83	16.12
19.70	18.13
15.76	14.02
17.00	14.04
13.96	16.20

Based on Boyer, D. M., Evans, A. R., and Jernvall, J. “Evidence of dietary differentiation among late Paleocene-Early Eocene Plesiadapids (Mammalia, Primates).” American Journal of Physical Anthropology, Vol. 142, © 2010 (Table).

Normal Curve Areas

z	.00	.01	.02	.03	.04	.05	.06	.07	.08	.09
.0	.0000	.0040	.0080	.0120	.0160	.0199	.0239	.0279	.0319	.0359
.1	.0398	.0438	.0478	.0517	.0557	.0596	.0636	.0675	.0714	.0753
.2	.0793	.0832	.0871	.0910	.0948	.0987	.1026	.1064	.1103	.1141
.3	.1179	.1217	.1255	.1293	.1331	.1368	.1406	.1443	.1480	.1517
.4	.1554	.1591	.1628	.1664	.1700	.1736	.1772	.1808	.1844	.1879
.5	.1915	.1950	.1985	.2019	.2054	.2088	.2123	.2157	.2190	.2224
.6	.2257	.2291	.2324	.2357	.2389	.2422	.2454	.2486	.2517	.2549
.7	.2580	.2611	.2642	.2673	.2704	.2734	.2764	.2794	.2823	.2852
.8	.2881	.2910	.2939	.2967	.2995	.3023	.3051	.3078	.3106	.3133
.9	.3159	.3186	.3212	.3238	.3264	.3289	.3315	.3340	.3365	.3389
1.0	.3413	.3438	.3461	.3485	.3508	.3531	.3554	.3577	.3599	.3621
1.1	.3643	.3665	.3686	.3708	.3729	.3749	.3770	.3790	.3810	.3830
1.2	.3849	.3869	.3888	.3907	.3925	.3944	.3962	.3980	.3997	.4015
1.3	.4032	.4049	.4066	.4082	.4099	.4115	.4131	.4147	.4162	.4177
1.4	.4192	.4207	.4222	.4236	.4251	.4265	.4279	.4292	.4306	.4319
1.5	.4332	.4345	.4357	.4370	.4382	.4394	.4406	.4418	.4429	.4441
1.6	.4452	.4463	.4474	.4484	.4495	.4505	.4515	.4525	.4535	.4545
1.7	.4554	.4564	.4573	.4582	.4591	.4599	.4608	.4616	.4625	.4633
1.8	.4641	.4649	.4656	.4664	.4671	.4678	.4686	.4693	.4699	.4706
1.9	.4713	.4719	.4726	.4732	.4738	.4744	.4750	.4756	.4761	.4767
2.0	.4772	.4778	.4783	.4788	.4793	.4798	.4803	.4808	.4812	.4817
2.1	.4821	.4826	.4830	.4834	.4838	.4842	.4846	.4850	.4854	.4857
2.2	.4861	.4864	.4868	.4871	.4875	.4878	.4881	.4884	.4887	.4890
2.3	.4893	.4896	.4898	.4901	.4904	.4906	.4909	.4911	.4913	.4916
2.4	.4918	.4920	.4922	.4925	.4927	.4929	.4931	.4932	.4934	.4936
2.5	.4938	.4940	.4941	.4943	.4945	.4946	.4948	.4949	.4951	.4952
2.6	.4953	.4955	.4956	.4957	.4959	.4960	.4961	.4962	.4963	.4964
2.7	.4965	.4966	.4967	.4968	.4969	.4970	.4971	.4972	.4973	.4974
2.8	.4974	.4975	.4976	.4977	.4977	.4978	.4979	.4979	.4980	.4981
2.9	.4981	.4982	.4982	.4983	.4984	.4984	.4985	.4985	.4986	.4986
3.0	.4987	.4987	.4987	.4988	.4988	.4989	.4989	.4989	.4990	.4990

Based on Table I of A. Hald, Statistical Tables and Formulas (New York: Wiley), 1952.

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 was the subject of research reported in the American Journal of Physical Anthropology (Vol. 142, 2010). These data are saved in the CHEEKTEETH file. A total of 18 cheek teeth extracted from skulls discovered in western Wyoming were analyzed. Each tooth was classified according to degree of wear (unworn, slight, light-moderate, moderate, moderate-heavy, or heavy). The 18 measurements are listed here.

Data on Degree of Wear
Unknown	Slight
Unknown	Slight
Unknown	Heavy
Moderate	Unworn
Slight	Light-moderate
Unknown	Light-moderate
Moderate-heavy	Moderate
Moderate	Unworn
Slight	Unknown

a. Identify the variable measured in the study and its type (quantitative or qualitative).
b. Count the number of cheek teeth in each wear category.
c. Calculate the relative frequency for each wear category.
d. Construct a relative frequency bar graph for the data.
e. Construct a Pareto diagram for the data.
f. Identify the degree of wear category that occurred most often in the sample of 18 cheek teeth.