Statistics 1: Covariance and Correlation Coefficient

Statistics 1
Statistics
Student’s Name
Student’s Number
University
Module Code
Module Name
Date

Statistics 2
Question 1
a.
X Y
y-
Ybar)sqd
5 20 -0.5 1.5 -0.75 0.25 2.25
3 23 -2.5 4.5 -11.25 6.25 20.25
7 15 1.5 -3.5 -5.25 2.25 12.25
9 11 3.5 -7.5 -26.25 12.25 56.25
2 27 -3.5 8.5 -29.75 12.25 72.25
4 21 -1.5 2.5 -3.75 2.25 6.25
6 17 0.5 -1.5 -0.75 0.25 2.25
8 14 2.5 -4.5 -11.25 6.25 20.25
Total 44 148 -89 42 192
Mean 5.5 18.5
Cov (x, y) = -89/8-1
= -89/7
= -12.71
b. The covariance between years of experience and salary is -12.71. A negative covariance
implies that the variables are inversely related (Stevens, 2012).
c.
r xy=cov (x , y )
sx s y

Statistics 3
Sx =
COV(x,y) = -12.71
SX = √42/7
= 2.45
SY = √192/7
=5.24
= -12.71/2.45 x 5.24
= -1
A correlation coefficient of -1 is an indication that for every positive increase in years of
experience there is a negative decrease of a fixed proportion in the salary (Cohen and Kohn,
2011).
d. A negative correlation implies that the relationship between years of experience and salary
is negative 100% of the time (Koo and Li, 2016; Mukaka, 2012).
Question 2
a.
H0: p = 0.1
H1: p≠ 0.1
b.
We calculate the test statistic;
p= 81/900
= 0.09
Z∗=p−po/(√po×(1−po)/n))
= 0.09 – 0.1 /√0.1 x0.9)/900))
= -0.01/√0.0004
= -0.01/0.02