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Magazine Chapter 7: Q. 21 (page 456)
More sample proportions List all possible SRSs of size n=, calculate 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 in Exercise . How does the variability of this sampling distribution compare with the variability of the sampling distribution from Exercise ? What does this indicate about increasing the sample size?
From exercise:
| Car Number | Color | Age |
| Red | ||
| White | ||
| Silver | ||
| Red |
Short Answer
Required dot plot is 
Dot plots with sample sizes of n=have less variability than dot plots with sample sizes of n=.
As the sample size grows, the sampling variability reduces.
Step by step solution
Given Information
We are given following data:
| Car Number | Color | Age |
| Red | ||
| White | ||
| Silver | ||
| Red | |
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
Explanation
All possible samples of size then contain any three cars all different of population of cars.
| Car Number | Color | Age |
| Red | ||
| White | ||
| Silver | ||
| Red |
The sample proportion of red cars is calculated by dividing the number of red cars by the sample size.
| Sample of size | Numbers of red cars | Proportion of red cars |
From above data our Dot plot will be:
In exercise dot plots varies in range of to , whereas in this problem dot plot ranges from to
As a result, dot plots with sample sizes of n= have less variability than dot plots with sample sizes of n= .
This also means that as the sample size grows, the sampling variability reduces.
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