Chapter 7: Q. 9 (page 454)

Sample proportions List all $10$ possible SRSs of size $n = 2$ , calculate the proportion of females for each sample, and display the sampling distribution of the sample proportion on a dotplot.

Short Answer

Expert verified

The proportion of females :

Sample of size $2$	Sample proportion of Female
Abigail - Bobby	$0.5$
Abigail - Carlos	$0.5$
Abigail - DeAnna	$1$
Abigail - Emily	$1$
Bobby - Carlos	$0$
Bobby - DeAnna	$0.5$
Bobby - Emily	$0.5$
Carlos - DeAnna	$0.5$
Carlos - Emily	$0.5$
DeAnna - Emily	$1$

The dotplot :

Step by step solution

Given information

We need to find proportion of females for each sample, and display the sampling distribution of the sample proportion on a dotplot for given table

Name	Gender	Quiz score
Abigail	Female	$10$
Bobby	Male	$5$
Carlos	Male	$10$
DeAnna	Female	$7$
Emily	Female	$9$

Simplify

As given Size of sample is two.

Therefore, the proportion of females for each sample :

Sample of size $2$	Sample proprtion of Female
Abigail - Bobby	$\hat{p} = \frac{1}{2} = 0.5$
Abigail - Carlos	$\hat{p} = \frac{1}{2} = 0.5$
Abigail - DeAnna	$\hat{p} = \frac{2}{2} = 1$
Abigail - Emily	$\hat{p} = \frac{2}{2} = 1$
Bobby - Carlos	$\hat{p} = \frac{0}{2} = 0$
Bobby - DeAnna	$\hat{p} = \frac{1}{2} = 0.5$
Bobby - Emily	$\hat{p} = \frac{1}{2} = 0.5$
Carlos - DeAnna	$\hat{p} = \frac{1}{2} = 0.5$
Carlos- Emily	$\hat{p} = \frac{1}{2} = 0.5$
DeAnna - Emily	$\hat{p} = \frac{2}{2} = 1$

A dot plot is a graph that shows the distribution of numerical variables by using dots to represent values.
If a value appears more than once in a whole number, the dots are stacked one on top of the other, with the height of the column of dots representing the frequency of that value.

The dot plot is :