Question

Three randomly selected households are surveyed. The numbers of people in the households are

11​,

22​,

and

1212.

Assume that samples of size

nequals=2

are randomly selected with replacement from the population of

11​,

22​,

and

1212.

Listed below are the nine different samples. Complete parts​ (a) through​ (c).

11​,11   

11​,22   

11​,1212   

22​,11   

22​,22   

22​,1212   

1212​,11   

1212​,22   

1212​,1212

  

a. Find the variance of each of the nine​ samples, then summarize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values.

s2		Probability
	0 0.3 1 0	nothing
	1 25 1 0.5	nothing
	▼ 25 50 100	nothing
	▼ 60.5 30.3 121	nothing

please show me a step by step to the answer

Answer 1

let first sample is x1 and 2nd sample is x2

x1	x2			s2
1	1			0
2	1			0.5
12	1			60.5
1	2			0.5
2	2			0
12	2			50
1	12			60.5
2	12			50
12	12			0

for 1st sample (1,1) , mean =(1+1)/2=1 ; therefore variance =(x-xbar)²/(n-1)

=((1-1)^2+(1-1)^2)/(2-1)=0

for 2nd sample (2,1) mean =(2+1)/2=1.5 ; therefore variance =(x-xbar)²/(n-1)

=((2-1.5)^2+(1-1.5)^2)/(2-1)=0.5

all other sample variance can be calculated in above manner:

therefore"

s2	probability
0	1/3
0.5	2/9
50	2/9
60.5	2/9