Question

Consider a population of size 4 who can be labelled as categories “A”, “A”, “B”, “C”, respectively. Let p ̂_A denote the sample proportion that fall into category “A” for a sample of size 3. Find the sampling distribution of p ̂_A.

Answer 1

Answer:

Given that,

Consider a population of size 4 who can be labelled as categories “A”, “A”, “B”, “C”, respectively.

Let denote the sample proportion that fall into category “A” for a sample of size

(3).

The sampling distribution of :

Sample	pA	Proportion
A,A,A	1/10	0.1
A,A,B	1/10	0.1
A,B,B	1/10	0.1
B,B,B	0/10	0
A,B,C	1/10	0.1
C,C,C	0/10	0
C,A,A	1/10	0.1
C,C,B	0/10	0
C,B,B	0/10	0
C,C,A	0/10	0