Question
In: Statistics and Probability
Look at the data from Table C6-3 relating to group rentals. -How many different samples of...
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 |
Solutions
Expert Solution
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.
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