Question

1. Consider the following table which shows different baskets of golf 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

Answer 1

(a)

Samples of Size 2	Mean of the sample
(1,2)	(30+18)/2 = 24
(1,3)	(30+30)/2 = 30
(1,4)	(30+33)/2 = 31.5
(1,5)	(30+36)/2 = 33
(2,3)	(18+30)/2 = 24
(2,4)	(18+33)/2 = 25.5
(2,5)	(18+36)/2 = 27
(3,4)	(30+33)/2 = 31.5
(3,5)	(30+36)/2 = 33
(4,5)	(33+36)/2 = 34.5

(b)

(i)

Mean of the distribution of the sample means () is given by:

(ii)

Population Mean () is given by:

(iii) We note that

Mean of the distribution of the sample means () = Population Mean ().

(c)

(i)

Dispersion ( )of population is given by:

(ii)

Dispersion () of distribution of sample means is given by:

We note :

Dispersion ( )of population is less than Dispersion () of distribution of sample means