Question

A student wonders if tall women tend to date taller men than do short

women. She measures herself, her dormitory roommate, and the women in the adjoining dorm rooms. Then she measures the next man each woman dates. Here are the data (heights in inches):

a. Make a scatterplot of these data. Describe what you see.

b. Find the correlation r step by step, using the formula on page 166. Explain how your value for r matches your description in part (a).

Short answer

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

Part (b) The value of $r$ is $0.5653$

Step-by-step solution

Part (a) Step 1: Given information

Part (a) Step 2: Explanation

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.

Part (b) Step 1: Calculation

The sample size $\left(n\right)$is $6$

The linear correlation coefficient $\left(r\right)$can be calculated as:

$$\begin{gathered} r=\frac{n\left(\Sigma xy\right)-\left(\Sigma x\right)\left(\Sigma y\right)}{\sqrt{\left(n\Sigma x^2{\left(\Sigma x\right)}^2\right)(n\Sigma y^2{\left(\Sigma y\right)}^2)}} \\ =\frac{6\left(27339\right)-\left(396\right)\left(414\right)}{\sqrt{\left(6\left(26158\right)-{\left(396\right)}^2\right)\left(6\left(28598\right)-{\left(414\right)}^2\right)}} \\ =0.5653 \end{gathered}$$

Thus, the value of $r$is $0.5653$