Answer to Question #128215 in Statistics and Probability for Richard Olarte

Question

Test the degree of association or significant relationship between the teaching
performance and management performance of the faculty members of school using the
Pearson product moment method at 0.05 level of significance. Give the decision.
Teachers Teaching
Performance
Management
Performance
A 3.6 3.8
B 4.4 3.9
C 4.1 2.0
D 4.0 2.8
E 4.0 2.9
F 3.4 3.0
G 2.8 4.5
H 4.9 3.3
I 3.6 2.9
J 3.0 3.0
K 3.5 3.8
L 3.0 2.7
M 4.3 3.2
N 3.2 3.3
O 4.3 3.4
P 3.4 4.1
Q 3.8 4.3
R 3.9 4.4
S 4.6 3.8
T 3.5 3.3

Answer 1

Solution

$r= \frac {(n(∑xy)-(∑x)(∑y))}{\sqrt{([n∑x^2-(∑x)^2][n∑y^2-(∑y)^2]})}$

$∑xy=257.06$

$∑x= 75.3$

$∑y= 68.4$

$∑x^2 = 289.59$

$∑y^2 = 241.86$

$n=20$

$r= \frac {(20*257.06-75.3*68.4)}{(\sqrt {([20*289.59- 75.3^2 ][20*241.86- 68.4^2])} )}$

$r= -0.06707$

The test statistic:

$t= \frac {(r \sqrt{(n-2)})}{\sqrt{(1- r^2 )}}$

$t= \frac{(-0.06707 * (20-2)^(0.5)}{\sqrt{(1- (-0.06707)^2 })}$

$= -0.2852$

The p-value given $t = -0.2852$ and $n-2=20-2=18$ degrees of freedom:

$p value=0.7789$

Answer: t value = - 0.0670

                The correlation is not significant since p value (0.7789) > significant level (0.05)