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 Whorls 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? (d) Biological anthropology is concerned with the comparative study of human origin, evolution, and diversity. Considering the sampling design in this study, to what population is it reasonable for the researchers to generalize their results?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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 |
| Whorls | 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.
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