Chapter 7.1, Problem 22E

To determine

To find: 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.

Answer to Problem 22E

Dot plot with sample size n = 3 has less variability than the dot plot with sample size n = 2

The sampling variability decreases as the sample size increases.

Explanation of Solution

Given:

Car number	color	Age
1	Red	1
2	White	5
3	Sliver	8
4	Red	20

Calculation:

All possible sample of size 3 is

Sample of size 3

1,2,3

1,2,4

1,3,4

2,3,4

The sample minimum is the smallest age of the three cars

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

Graph:

  

Variability

In the previous exercise, the dots in the dot plots range from 1 to 8.

The dots in the above dot plot range from 1 to 5.

This then means that the dot plot with sample size $n=3$ has less variability than the dot plot with sample size $n=2$ (as the range of the dots is smaller).

This then is also indicating that the sampling variability decreases as the sample size increases.