Question

Are fingerprint patterns genetic, or are they developmental? In 1892 Francis Galton compiled the following table on the relationship between the patterns on the same finger of 105 sibling pairs. Test the hypothesis that the patterns are independent for example, that knowing one sibling (A) has a Whorl on the finger does not help in predicting the pattern of the other (B).

A children

B children	Arches	Loops	Whorls	Totals
Arches	5	12	2	19
Loops	4	42	15	61
Whorls	1	14	10	24
Totals	10	68	27	105

Answer 1

H0: Null Hypothesis: The patterns are independent

HA: Alternative Hypothesis: The patterns are dependent.

Under assumption of H0, the Expected Frequencies are obtained as follows:

	Arches	Loops	Whorls	Total
Arches	10X19/105=1.81	12.30	4.89	19
Loops	5.81	39.50	15.69	61
Whorls	2.38	16.19	6.43	25
Total	10	68	27	105

From the above Table, the Table is calculated as follows:

O	E	(O - E)2/E
5	1.81	5.63
12	12.30	0.01
2	4.89	1.70
4	5.81	0.56
42	39.50	0.16
15	15.69	0.03
1	2.38	0.80
14	16.19	0.30
10	6.43	1.98
Total = =		11.17

= 11.17

ndf = ( r - 1) X (c - 1)

    = (3 - 1) X (3 - 1) = 4

By Technology, p- value = 0.0247

Since p - value = 0.0247 is less than = 0.05, the difference is significant. Reject null hypothesis.

Conclusion:
The data do not support the claim that the patterns are independent.