Question

Question 1. Given the following table answer the questions.

                          Score

Respondent          X            Y         x-x       (x-x) ²         y-y      ( y-y) ²     ( x-x) ( y-y)

A. Rose                 18          92   

B. Bush                 36          65    

C. Novicevic         24          91

D. Vitell                28          85                                                                       

E. Walker              25          70    

a. Calculate Pearson’s Product Movement Correlation Coefficient (r). Show your work.

b. Based on the correlation coefficient which you calculated, in two words how would you describe the relationship between the two variables in the “test”?

Question 2. PHR Score

               Score

Respondent        X             Y         x-x       (x-x) ²         y-y      ( y-y) ²     ( x-x) ( y-y)

A. Selber           96            92

B. Franklin         56            65

C. Nichols          84            91   

D. Vitello           88            85

E. Grado           72            70

a. Calculate Pearson’s Product Movement Correlation Coefficient (r). Show your work.

b. Based on the correlation coefficient which you calculated, in two words how would you describe the relationship between the two variables in the “test”?

Question 3. Which of the two “tests” above would you choose? Why?

Answer 1

1.

X Values
∑ = 131
Mean = 26.2
∑(X - M_x)² = SS_x = 172.8

Y Values
∑ = 403
Mean = 80.6
∑(Y - M_y)² = SS_y = 613.2

X and Y Combined
N = 5
∑(X - M_x)(Y - M_y) = -248.6

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = -248.6 / √((172.8)(613.2)) = -0.7637

b. Hence we see that there is negative correlation between X and Y

2.

X Values
∑ = 396
Mean = 79.2
∑(X - M_x)² = SS_x = 972.8

Y Values
∑ = 403
Mean = 80.6
∑(Y - M_y)² = SS_y = 613.2

X and Y Combined
N = 5
∑(X - M_x)(Y - M_y) = 718.4

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 718.4 / √((972.8)(613.2)) = 0.9302

b. There is strong positive correlation between x and y

3. As r is strong for second test, we will prefer it.