Fingerprint analysis and blood grouping are features that do not change through the lifetime of an individual. Fingerprint features appear early in the development of a fetus, and blood types are determined by genetics. Therefore, each is considered an effective tool for identification of individuals. These characteristics are also of interest in the discipline of biological anthropology—a scientific discipline concerned with the biological and behavioral aspects of human beings. The relationship between these characteristics was the subject of a study conducted by biological anthropologists with a simple random sample of male students from a certain region with a large student population. Fingerprint patterns are generally classified as loops, whorls, and arches. The four principal blood types are designated as A, B, AB, and O. The table shows the distribution of fingerprint patterns and blood types for the sample. Expected counts are listed in parentheses. The anthropologists were interested in the possible association between the variables. Blood Type A B AB O Total Loops 66 (71.69) 99 (112.19) 35 (32.29) 101 (84.83) 301 Whirls 51 (47.16) 91 (73.80) 15 (21.24) 41 (55.80) 198 Arches 14 (12.15) 15 (19.01) 9 (5.47) 13 (14.37) 51 Total 131 205 59 155 550 (a) Is the test for an association in this case a chi-square test of independence, or a chi-square test of homogeneity? Justify your choice. (b) Identify the conditions for the chi-square inference procedure selected in part (a), and indicate whether the conditions are met. (c) The resulting chi-square test statistic from the appropriate test is approximately 18.930. What are the degrees of freedom and p-value of the test?
) Fingerprint analysis and blood grouping are features that do not change through the lifetime of an individual. Fingerprint features appear early in the development of a fetus, and blood types are determined by genetics. Therefore, each is considered an effective tool for identification of individuals. These characteristics are also of interest in the discipline of biological anthropology—a scientific discipline concerned with the biological and behavioral aspects of human beings.
The relationship between these characteristics was the subject of a study conducted by biological anthropologists with a simple random sample of male students from a certain region with a large student population. Fingerprint patterns are generally classified as loops, whorls, and arches. The four principal blood types are designated as A, B, AB, and O. The table shows the distribution of fingerprint patterns and blood types for the sample. Expected counts are listed in parentheses. The anthropologists were interested in the possible association between the variables.
|
|
|
Blood Type |
|
|
|
|
|
A |
B |
AB |
O |
Total |
|
Loops |
66 (71.69) |
99 (112.19) |
35 (32.29) |
101 (84.83) |
301 |
|
Whirls |
51 (47.16) |
91 (73.80) |
15 (21.24) |
41 (55.80) |
198 |
|
Arches |
14 (12.15) |
15 (19.01) |
9 (5.47) |
13 (14.37) |
51 |
|
Total |
131 |
205 |
59 |
155 |
550 |
(a) Is the test for an association in this case a chi-square test of independence, or a chi-square test of homogeneity? Justify your choice.
(b) Identify the conditions for the chi-square inference procedure selected in part (a), and indicate whether the conditions are met.
(c) The resulting chi-square test statistic from the appropriate test is approximately 18.930. What are the degrees of freedom and p-value of the test?
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