Question

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

Short answer

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	$\hat{\mathrm{p}}=\frac{1}{2}=0.5$
Abigail - Carlos	$\hat{\mathrm{p}}=\frac{1}{2}=0.5$
Abigail - DeAnna	$\hat{\mathrm{p}}=\frac{2}{2}=1$
Abigail - Emily	$\hat{\mathrm{p}}=\frac{2}{2}=1$
Bobby - Carlos	$\hat{\mathrm{p}}=\frac{0}{2}=0$
Bobby - DeAnna	$\hat{\mathrm{p}}=\frac{1}{2}=0.5$
Bobby - Emily	$\hat{\mathrm{p}}=\frac{1}{2}=0.5$
Carlos - DeAnna	$\hat{\mathrm{p}}=\frac{1}{2}=0.5$
Carlos- Emily	$\hat{\mathrm{p}}=\frac{1}{2}=0.5$
DeAnna - Emily	$\hat{\mathrm{p}}=\frac{2}{2}=1$

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 :

From dot plot

Centre $=0.5$

Minimum $=0$

Maximum $=1$

Range $=1$

Distribution is slightly negative of left skewed.