Chapter 3.1, Problem 22E

(a)

To determine

To construct:The scatterplot of data set.

Explanation of Solution

Given:

Women(x)	Men(y)
66	72
64	68
66	70
65	68
70	71
65	65

Construction:

There are the following steps into excel.

• Put the data into excel sheet.
• Click on Insert.
• Select the data set.
• Click on Scatter.

  

It appears that there is a positive correlation between women and men.

(b)

To determine

To conclude:The correlation between the men and women.

Answer to Problem 22E

Explanation of Solution

Give:

As per the above given information,

Calculation:

Women(x)	Men(y)	x2	y2	xy
66	72	4356	5184	4752
64	68	4096	4624	4352
66	70	4356	4900	4620
65	68	4225	4624	4420
70	71	4900	5041	4970
65	65	4225	4225	4225
${\displaystyle \sum x}=396$	${\displaystyle \sum y}=414$	${\displaystyle \sum x^2}=26158$	${\displaystyle \sum y^2}=28598$	${\displaystyle \sum xy}=27339$

The sample size (n) is 6.

The linear correlation coefficient (r), can be calculated as: $\begin{array}{c}r=\frac{n\left({\displaystyle \sum xy}\right)-\left({\displaystyle \sum x}\right)\left({\displaystyle \sum y}\right)}{\sqrt{\left(n{\displaystyle \sum x^2-{\left({\displaystyle \sum x}\right)}^2}\right)\left(n{\displaystyle \sum y^2-{\left({\displaystyle \sum y}\right)}^2}\right)}}\\ =\frac{6\left(27339\right)-\left(396\right)\left(414\right)}{\sqrt{\left(6\left(26158\right)-{\left(396\right)}^2\right)\left(6\left(28598\right)-{\left(414\right)}^2\right)}}\\ =0.5653\end{array}$

Thus, the value of r is 0.5653.