Chapter 7.1, Problem 21E

To determine

To find: the proportion of red cars in the sample, and display the sampling distribution of the sample proportion on a dot plot with the same scale as the dot plot and the variability of this sampling distribution compare with the variability of the sampling distribution and find the indicate about increasing the sample size.

Answer to Problem 21E

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 proportion of red cars is

Sample of size 3	Number of red cars	Proportion of red cars
1,2,3	1	$\widehat{p}=\frac{1}{3}$
1,2,4	2	$\widehat{p}=\frac{2}{3}$
1,3,4	2	$\widehat{p}=\frac{2}{3}$
2,3,4	1	$\widehat{p}=\frac{1}{3}$

Graph:

  

For every given data value places a dot above the associating number on the number line.

Variability

The dots in the above dot plot range from $\frac{1}{3}=0.3333$ to $\frac{2}{3}=0.6667$

This then implies that the dot plot with sample size $n=3$ has less variability than the dot plot with sample size $n=2$

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