Question

6. In a recent study investigating a possible genetic link between individuals’ susceptibility to developing symptoms of AIDS, 549 men who had been diagnosed HIV positive were classified according to whether they carried two particular alleles (DRB1*0702 and DQA1*0201). The results were as follows:

Condition of individual Free of symptoms Early symptoms Suffering from AIDS

Alleles present 24 7 17

Alleles absent 98 93 310

Use these results to test whether there is an association between the presence of the alleles and the classification into the three AIDS statuses.

Answer 1

H0: Null Hypothesis:There is no association between presence of the alleles and the classification into the three AIDS statuses

HA: Alternative Hypothesis:There is association between presence of the alleles and the classification into the three AIDS statuses

Observed Frequencies:

	Free of symptoms	Early symptoms	Suffering from AIDS	Total
Alleles present	24	7	17	48
Alleles absent	98	93	310	501
Total	122	100	327	549

Assuming H0, Expected Frequencies are calculated as follows:

Observed Frequencies:

	Free of symptoms	Early symptoms	Suffering from AIDS	Total
Alleles present	122X48/549=10.67	8.74	28.59	48
Alleles absent	111.33	91.26	298.41	501
Total	122	100	327	549

statistic is calculated as follows:

O	E	(O - E)2/E
24	10.67	16.67
7	8.74	0.35
17	28.59	4.70
98	111.33	1.60
93	91.26	0.03
310	298.41	0.45
Total = =		23.79

So,

Test statistic = 23.79

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

   = (2 - 1) X (3-1) = 2

By Technology, p - value is < 0.00001

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

Conclusion:

The data support the claim that there is association between presence of the alleles and the classification into the three AIDS statuses