Chapter 7.1, Problem 9E

To determine

To Calculate: the mean quiz score for each sample and display the sampling distribution of the sample mean on dot plot.

Answer to Problem 9E

Sample of size 2	Sample proportion of the female
Abigail-Bobby	0.5
Abigail-Carlos	0.5
Abigail-De Anna	1
Abigail-Emily	1
Bobby-Carlos	0
Bobby-De Anna	0.5
Bobby-Emily	0.5
Carlos-De Anna	0.5
Carlos-Emily	0.5
De Anna-Emily	1

Explanation of Solution

Given:

Name	Gender	Quiz Score
Abigail	Female	10
Bobby	Male	5
Carlos	Male	10
De Anna	Female	7
Emily	Female	9

Formula used:

Sample of size 2	Sample proportion of female
Abigail-Bobby	$\widehat{p}=\frac{1}{2}=0.5$
Abigail-Carlos	$\widehat{p}=\frac{1}{2}=0.5$
Abigail-De Anna	$\widehat{p}=\frac{2}{2}=1$
Abigail-Emily	$\widehat{p}=\frac{2}{2}=1$
Bobby-Carlos	$\widehat{p}=\frac{0}{2}=0$
Bobby-De Anna	$\widehat{p}=\frac{1}{2}=0.5$
Bobby-Emily	$\widehat{p}=\frac{1}{2}=0.5$
Carlos-De Anna	$\widehat{p}=\frac{1}{2}=0.5$
Carlos-Emily	$\widehat{p}=\frac{1}{2}=0.5$
De Anna-Emily	$\widehat{p}=\frac{2}{2}=1$

Graph:

  

By seeing the dot plot, it is observed that centre is at about 0.50 and minimum and maximum values are 0 and 1 respectively so the range is 1 and the distribution looks slightly negative of left skewed.