Question

Look at the data from Table C6-3 relating to group rentals.

-How many different samples of 3 are possible?

-List all possible samples of size 3, and compute the mean number of group rental

instances in each sample.

-Compare the mean of the distribution of sample means to the population mean.

Group	Times Rented for Group
Yuka Youthsports	3
American Hackers' Society	6
Taggert's Tours	3
Gattaca University	1
Silvertown Senior Center	3
City Works	0

Answer 1

Total number of groups = 6

Sample size = 3

Hence number of all possible of size 3 is ⁶C₃ = 20

Consider

Yuka Youthsports : 1

American Hacker's society : 2

Taggert's house : 3

Gattaka University : 4

Silvertown Senior Center : 5

City works : 6

sample mean = sample total / 3.

Group	Times Rented for Group (X)	Group No.	Sample Size of 3	time	Sample total	Sample Mean(Xbar)
Yuka Youthsports	3	1	(1,2,3)	3,6,3	12	4.0000
American Hackers' Society	6	2	(1,2,4)	3,6,1	10	3.3333
Taggert's Tours	3	3	(1,2,5)	3,6,3	12	4.0000
Gattaca University	1	4	(1,2,6)	3,6,0	9	3.0000
Silvertown Senior Center	3	5	(1,3,4)	3,3,1	7	2.3333
City Works	0	6	(1,3,5)	3,3,3	9	3.0000
Total	16		(1,3,6)	3,3,0	6	2.0000
			(1,4,5)	3,1,3	7	2.3333
			(1,4,6)	3,1,0	4	1.3333
			(1,5,6)	3,3,0	6	2.0000
			(2,3,4)	6,3,1	10	3.3333
			(2,3,5)	6,3,3	12	4.0000
			(2,3,6)	6,3,0	9	3.0000
			(2,4,5)	6,1,3	10	3.3333
			(2,4,6)	6,1,0	7	2.3333
			(2,5,6)	6,3,0	9	3.0000
			(3,4,5)	3,1,3	7	2.3333
			(3,4,6)	3,1,0	4	1.3333
			(3,5,6)	3,3,0	6	2.0000
			(4,5,6)	1,3,0	4	1.3333
					Total	53.3333

The mean of disribution of sample mean is

The population mean ( ) is given by

Since

Hence sample mean is an unbiased estimator of population mean.