Question

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

2,

4​,

and

12.

Assume that samples of size

nequals=2

are randomly selected with replacement from the population of

2​,

4​,

and

12.

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

2,2​,

2,4​,

2​,12 

4,12

12,2

12,4

12,12

  

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.

Answer 1

a) below is variance distribution:

x1	x2	P(x1,x2)		s2
2	2	1/9		0
4	2	1/9		2
12	2	1/9		50
2	4	1/9		2
4	4	1/9		0
12	4	1/9		32
2	12	1/9		50
4	12	1/9		32
12	12	1/9		0

from above:

s2	probability
0	1/3
2	2/9
32	2/9
50	2/9