Chapter 7.1, Problem 7E

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 7E

Sample of size 2	Sample mean
Abigail-Bobby	7.5
Abigail-Carlos	10
Abigail-De Anna	8.5
Abigail-Emily	9.5
Bobby-Carlos	7.5
Bobby-De Anna	6
Bobby-Emily	7
Carlos-De Anna	8.5
Carlos-Emily	9.5
De Anna-Emily	8

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 mean
Abigail-Bobby	$\overline{x}=\frac{10+5}{2}=7.5$
Abigail-Carlos	$\overline{x}=\frac{10+10}{2}=10$
Abigail-De Anna	$\overline{x}=\frac{10+7}{2}=8.5$
Abigail-Emily	$\overline{x}=\frac{10+9}{2}=9.5$
Bobby-Carlos	$\overline{x}=\frac{5+10}{2}=7.5$
Bobby-De Anna	$\overline{x}=\frac{5+7}{2}=6$
Bobby-Emily	$\overline{x}=\frac{5+9}{2}=7$
Carlos-De Anna	$\overline{x}=\frac{10+7}{2}=8.5$
Carlos-Emily	$\overline{x}=\frac{10+9}{2}=9.5$
De Anna-Emily	$\overline{x}=\frac{7+9}{2}=8$

Graph:

  

By seeing the dot plot, it is observed that centre is at about 8.25 and minimum and maximum values are 6 and 10 respectively so the range is 4 and the distribution looks slightly negative of left skewed.