Statistics for Business Assignment

Assessment 1 - Assignment
Unit:STA101 – Statistics for Business
Student Name:
Student Number:
Course Instructor:
Date: 19th January 2019

Question 1:
A sample of eight observations of variables x (years of experience) and y (salary in $1,000s)
is shown below:
x 5 3 7 9 2 4 6 8
y 20 23 15 11 27 21 17 14
a. Calculate and interpret the covariance between x and y.
Answer
Cov ( X , Y ) =
∑
i=1
n
( Xi−X ) ( Y i−Y )
n
X =
∑
i =1
n
Xi
n =5+ 3+7+9+2+ 4+ 6+8
8 = 44
8 =5.5
Y =
∑
i=1
n
Y i
n = 20+23+15+11+27 +21+17+14
8 =148
8 =18 .5
Cov ( X , Y ) =
∑
i=1
n
( Xi−X ) ( Y i−Y )
n
¿ ( 5−5.5 ) ( 20−18.5 ) +...+ ( 8−5.5 ) ( 14−18.5 )
8 =−89
8 =−11.125
b. Give a possible reason that the covariance is negative.
Answer
A possible reason as to why the covariance is negative is that the relationship
between x and y is negative. X and Y move in an inverse direction.
c. Calculate the coefficient of correlation, and comment on the relationship
between x and y.
Answer
r = Cov ( X ,Y )
SD ( X ) SD(Y )

SD ( X )= √ ∑
i=1
n
( Xi− X )2
n−1 = √ ( 5−5.5 )2 + ( 3−5.5 )2+ (6−5.5 )2 + ( 8−5.5 )2
7 = √ 42
7 = √6=2.4495
SD ( Y )= √ ∑
i=1
n
( Y i−Y )2
n−1 = √ ( 20−18 .5 )2 + ( 23−18 .5 )2 + ( 17−18.5 )2+ (14−18 .5 )2
7 = √ 19 2
7 = √27.42857=5.23
r = Cov ( X ,Y )
SD ( X ) SD(Y )= −11.125
2.4495∗5.237229 =−0.86721
d. Give a possible reason that the correlation is negative.
Answer
The possible reason that the correlation is negative is the fact that the
relationship between x and y is negative. X and Y move in an inverse
direction.
Question 2:
A company claims that 10% of the users of a certain sinus drug experience drowsiness. In
clinical studies of this sinus drug, 81 of the 900 subjects experienced drowsiness.
a. We want to test their claim and find out whether the actual percentage is not 10%. State
the appropriate null and alternative hypotheses.
Answer
H0: The proportion of users who use sinus drug and experience drowsiness is 10%
HA: The proportion of users who use sinus drug and experience drowsiness is not 10%
This can also be written as follows;
H0 : p=0.1
H A : p ≠ 0.1
b. Is there enough evidence at the 5% significance level to infer that the competitor is
correct?
Answer
We compute the Z statistics as follows;
Z= ^p− p
√ p (1− p )
n