Question

1. Consider the following table which shows different baskets of tennis balls:

Baskets	Number of golf balls (Population)
1	30
2	18
3	30
4	33
5	36

(a) List all samples of size 2, and compute the mean of each sample.

(b) Compute the mean of the distribution of the sample mean and the population mean. Compare the two values.

(c) Compare the dispersion in the population with that of the sample mean.

PLEASE SHOW ALL WORK

Answer 1

a)

Total possible pairs of sample size 2 are

Basket 1	Basket 2	Mean
30	18	24
30	30	30
30	33	31.5
30	36	33
18	30	24
18	33	25.5
18	36	27
30	33	31.5
30	36	33
33	36	34.5

b)

The population mean is obtained as follow,

Baskets	Number of golf balls
1	30
2	18
3	30
4	33
5	36
Mean	29.4

The sample mean for all possible sample of size two is obtained as follow,

Sample	Mean
1	24
2	30
3	31.5
4	33
5	24
6	25.5
7	27
8	31.5
9	33
10	34.5
mean	29.4

Sample mean and the population mean are same.

c)

The dispersion in the mean in define by the standard deviation,

Baskets	Number of golf balls, x	Population mean,
1	30	29.4	0.6	0.36
2	18	29.4	-11.4	129.96
3	30	29.4	0.6	0.36
4	33	29.4	3.6	12.96
5	36	29.4	6.6	43.56
			Sum	187.2

The sample mean is obtained as follow,

Sample	Mean, x	Sample mean,
1	24	29.4	-5.4	29.16
2	30	29.4	0.6	0.36
3	31.5	29.4	2.1	4.41
4	33	29.4	3.6	12.96
5	24	29.4	-5.4	29.16
6	25.5	29.4	-3.9	15.21
7	27	29.4	-2.4	5.76
8	31.5	29.4	2.1	4.41
9	33	29.4	3.6	12.96
10	34.5	29.4	5.1	26.01
			Sum	140.4

The population mean is more dispersed compare to sample mean