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Chapter 3: Q.20 (page 161)

Data on dating 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 rooms. Then she measures the next man each woman dates. Here are the data (heights in inches):

(a) Make a scatterplot of these data. Based on the scatterplot, do you expect the correlation to be positive or negative? Near 卤1or not?

(b) Find the correlation r step-by-step. First, find the mean and standard deviation of each variable. Then find the six standardized values for each variable. Finally, use the formula for r. Do the data show that taller women tend to date taller men?

Short Answer

Expert verified

a). The correlation should be positive.

b). The value ofr=0.5653.

Step by step solution

01

Part(a) Step 1: Given Information

Data:

02

Part(a) Step 2: Explanation 

Women (x)is on the horizontal axis, and Men (y)is on the vertical axis.

03

Part(a) Step 3: Explanation

The scatterplot slopes upwards, indicating that the correlation should be positive.

Because the points do not appear to be on the same axis, the correlation should be less than卤1.

04

Part(b) Step 1: Given Information 

Data:

05

Part(b) Step 2: Explanation 

To find X路Y,X2and Y2as it was done in the table below.

06

Part (b) Step 3: Explanation 

Find the sum of every column to get:

鈭�X=396,鈭�Y=414,鈭�X路Y=27339,鈭�X2=26158,鈭�Y2=28598

To calculate the correlation coefficient, use the formula below.

localid="1649931991616" r=n路鈭�XY-鈭�X路鈭�Yn鈭�X2-鈭�X2路n鈭�Y2-鈭�Y2=6鈰�27339鈭�396鈰�4146鈰�26158鈭�3962鈰�6鈰�28598鈭�4142鈮�0.5653

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