Example 11.10: It is important that scientific researchers in the area of forest products be able to study correlation among the anatomy and mechanical properties of trees. For the study Quantitative Anatomical Characteristics of Plantation Grown Loblolly Pine (Pinus Taeda L.) and Cottonwood (Populus deltoides Bart. Ex Marsh.) and Their Relationships to Mechanical Properties, conducted by the Department of Forestry and Forest Products at Virginia Tech, 29 loblolly pines were randomly selected for investigation. Table 11.9 shows the resulting data on the specific gravity in grams/cm3 and the modulus of rupture in kilopascals (kPa). Compute and interpret the sample correlation coefficient.
Table 11.9: Data on 29 Loblolly Pines for Example
Specific Gravity,
Modulus of Rupture,
x (g/cm3)
y (kPa)
0.414
29,186
0.581
85,156
0.383
29,266
0.557
69,571
0.399
26,215
0.550
84,160
0.402
30,162
0.531
73,466
0.442
38,867
78,610
0.422
37,831
0.556
67,657
0.466
44,576
0.523
74,017
0.500
46,097
0.602
87,291
0.514
59,698
0.569
86,836
0.530
67,705
0.544
82,540
66,088
81,699
0.558
78,486
82,096
0.577
89,869
0.547
75,657
0.572
77,369
0.585
80,490
0.548
67,095
For the data of Example 11.10, test the hypothesis that there is no linear association among the variables.
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