Question

A box contains 6 balls labeled form 0 to 5. Three balls are drawn without replacement. Construct the sampling distribution of the following sample statistics of the labels of the balls drawn.

A.sample mean

B.sample range

C.sample max (the highest number in a set)

D.sample min (the lowest numbef in a set)

Answer 1

The number of possible samples of size n=3 from a population of size N=6 is,

$=C_6^3= \binom{6}{3}=20$

The sample means are derived from the formula, $\bar x_i={\sum x_i\over3}$

​(a) The samples and their means are shown in the table below.

The sampling distribution of the sample means are given below.

(b) The sample ranges are given in the table below

and the sampling distribution of the sample ranges given below.

(c) The sample max

and the sampling distribution of the sample max

(d) The sample min

and the sampling distribution of the sample min