Question

More sample minimums List all $4$possible SRSs of size n=$3$, calculate the minimum age for each sample, and display the sampling distribution of the sample minimum on a dot plot with the same scale as the dot plot in Exercise $20$. How does the variability of this sampling distribution compare with the variability of the sampling distribution from Exercise $20$? What does this indicate about increasing the sample size?

From exercise$20$:

Car Number	Color	Age
$1$	Red	$1$
$2$	White	$5$
$3$	Silver	$8$
$4$	Red	$20$

Short answer

Dot plots with sample sizes of n=$3$have less variability than dot plots with sample sizes of n=.

As the sample size grows, the sampling variability reduces.

Dot plot:

Step-by-step solution

Given Information

We are given following data:

Car Number	Color	Age
$1$	Red	$1$
$2$	White	$5$
$3$	Silver	$8$
$4$	Red	$20$

We need to calculate the minimum age for each sample, and draw it's dot plots.

We need to explain how variability of this sampling distribution compare with the variability of the sampling distribution from Exercise$20$

Explanation

All possible samples of size $3$then contain any three cars all different of population of $4$cars.

Sample of size $3$

$1,2,3$

$1,3,4$

$1,2,4$

$2,3,4$

The smallest age of three cars is used as a sample minimum

Sample of size $3$	Sample minimum
$1,2,3$	min($1,5,8$) = $1$
$1,2,4$	min($1,5,20$) = $1$
$1,3,4$	min($1,8,20$) = $1$
$2,3,4$	min($5,8,20$) = $5$

From above data our Dot plot will be:

In exercise $20$dot plots varies in range of $1$to $8$, whereas in this problem dot plot ranges from $1$to $5$

As a result, dot plots with sample sizes of n=$3$have less variability than dot plots with sample sizes of n=$2$.

This also means that as the sample size grows, the sampling variability reduces.