Question

A recent bulletin issued by a large blood bank claims four blood types are distributed in the U.S. population according to the following proportions:

.44 are type O

.42 are type A

.10 are type B

.04 are type AB

To determine whether blood types are distributed in the same way in a population of AIDS patients, a random sample of 100 AIDS patients is obtained. If the distribution of blood types is different, something having to do with blood types may be associated with susceptibility to the AIDS virus.

Blood Type Data
Blood Type	O	A	B	AB
Frequency	38	38	20	4

The research question is, "Is the distribution of blood types in the AIDS patients different from the distribution of blood types in the general population."

A) State the null hypothesis (H0).

B) State the alternative (research) hypothesis (HA).

C) The degrees of freedom (df) for the test are:

D) The critical region is: (determined by ?, from ?2-table)

E) The brief table below arranges the basic data needed for the 100 subjects so as to organize and facilitate computations.

Observed (Oj) & Expected (Ej) Frequencies
Blood Type		O	A	B	AB
Frequency	Expected	E1 = .44(100) = 44	E2 = .42(100) = 42	E3 = ?	E4 = ?
	Observed	O1 = 38	O2 = 38	O3 = 20	O4 = 4
Now You're Ready to Compute the Ej's & ?2: ?2 = ?(Oj - Ej)2/Ej

The expected frequency, E4 is ??

F)The brief table below arranges the basic data needed for the 100 subjects so as to organize and facilitate computations.

Observed (Oj) & Expected (Ej) Frequencies
Blood Type		O	A	B	AB
Frequency	Expected	E1 = .44(100) = 44	E2 = .42(100) = 42	E3 = ?	E4 = ?
	Observed	O1 = 38	O2 = 38	O3 = 20	O4 = 4
Now You're Ready to Compute the Ej's & ?2: ?2 = ?(Oj - Ej)2/Ej

Do you reject or retain the null hypothesis (H0)? (Is the computed value of ?2 in the critical region ( ?2 ? 7.815)?)

a)Reject H0. Blood types for AIDS patients are distributed as hypothesized.

b)Reject H0. Blood types for AIDS patients are not distributed as hypothesized.

c)Retain H0. Blood types for AIDS patients are distributed as hypothesized.

d)Retain H0. Blood types for AIDS patients are not distributed as hypothesized.

Answer 1

A)

The null hypothesis is:

H0: The blood types are distributed in the same way in a population of AIDS patients.

B)

The alternative hypothesis is:

H0: The blood types are not distributed in the same way in a population of AIDS patients.

C)

There are 4 blood types so degree of freedom is:

df=4-1=3

D)

Let

The critical value is: 7.815

E)

Following table shows the calculations:

	O	p	E=100*p	(O-E)^2/E
	38	0.44	44	0.818181818
	38	0.42	42	0.380952381
	20	0.1	10	10
	4	0.04	4	0
Total	100		100	11.1991342

So,

Since test statistics is greater than critical value so we reject the null hypothesis.

Decision:

b)Reject H0. Blood types for AIDS patients are not distributed as hypothesized.