Respuesta :
Answer:
n=6 [tex] \sum x = 396, \sum y = 421, \sum xy = 27809, \sum x^2 =26158, \sum y^2 =29569[/tex]
[tex]r=\frac{6(27809)-(396)(421)}{\sqrt{[6(26158) -(396)^2][6(29569) -(421)^2]}}=0.913[/tex]
So then the correlation coefficient would be r =0.913
And as we can see the value for r is very high and near to 1. so the correct option for this case would be:
C. There is a positive correlation between the heights of men and women.
Step-by-step explanation:
Previous concepts
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
And in order to calculate the correlation coefficient we can use this formula:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
We have the following data:
Women (X): 66 64 66 65 70 65
Men(Y): 72 68 70 68 74 69
We have quantitative data so no makes sense say that we have categorical data.
For our case we have this:
n=6 [tex] \sum x = 396, \sum y = 421, \sum xy = 27809, \sum x^2 =26158, \sum y^2 =29569[/tex]
[tex]r=\frac{6(27809)-(396)(421)}{\sqrt{[6(26158) -(396)^2][6(29569) -(421)^2]}}=0.913[/tex]
So then the correlation coefficient would be r =0.913
And as we can see the value for r is very high and near to 1. so the correct option for this case would be:
C. There is a positive correlation between the heights of men and women.
