Statistics Question Solution 2022

STATISTICS
STUDENT ID:
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Question 1
a) The requisite scatter plot is shown below.
15 20 25 30 35 40 45 50 55
0
5
10
15
20
Scatter Plot
Percent GM
Cars Sold (million)
From the downward sloping trend line, it is evident that the relationship between Percent GM
and Cars Sold is negative. This implies that it is observed that when one of the variables is
higher, the other is lower. Further, based on the positioning of the scatter points around the
trend line, it may be concluded that the strength of the linear association seems medium to
high.
b) The correlation coefficient has been computed using MS-Excel and has come out as -
0.7468. The negative sign of the correlation coefficient suggests that the two underlying
variables are inversely proportional. Also, the magnitude of the correlation coefficient is
quite high which would indicate that the strength of association between the two variables
is quite strong.
Question 2
a) The requisite scatter plot is shown below.

0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
Scatter Plot
Months Owned
Hours Exercise
From the above scatter plot, there seems be a negative or inversely proportional relationship
between the given variables as the points seem to be arranged in the form of a downward
sloping line. Also, the extent of linear association seems high considering the low deviation
of scatter points from the linear trend which is broadly emerging.
b) The requisite computation of correlation coefficient is shown below.
Let number of months be X while hours exercised be Y
Mean X ̄¿ = (12+.....+5)/10 = 6.5
Standard deviation Sx= √ 1
10−1 { ( 12−6.5 ) 2+ ... .+ ( 5−6.5 ) 2 }=3.3417
Similarly,
Mean Y ̄¿= (4+.....+5)/10 = 5.8
Standard deviation Sy= √ 1
10−1 { ( 4−5.8 )2 +... .+ ( 5−5.8 )2 }=2.5734
Correlation coefficient
R=∑ ¿ ¿ ¿
R= ( 12−6.5 )∗( 4−5.8 ) +...+ ( 5−6.5 )∗( 5−5.8 )
( 10−1 )∗3.3417∗02.5734 =−0.8269