Question

Are the marks one receives in a course related to the amount of time spent studying the subject? To analyze this mysterious possibility, a student took a random sample of 10 students who had enrolled in an accounting class last semester. He asked each to report his or her mark in the course and the total number of hours spent studying accounting. These data are listed here.
Marks

Time Spent Studying

77

40

63

42

79

37

86

47

51

25

78

44

83

41

90

48

65

35

47

28

Enlarge Table

a.

Calculate the covariance.

b.

Calculate the coefficient of correlation.

c.

What do the statistics calculated above tell you about the relationship between marks and study time?

A. First, do the calculations for covariance and coefficient of correlation using only Excel's add/Sum, subtract, multiply, divide functions (OK, use ^2 (to square a number) )
B. Then calculate the covariance and coefficient of correlation using Excel's CORREL and COVAR functions
C. What do the statistics calculated above tell you about the relationship between marks and study time?

Answer 1

Answer:

a) 98.522

b) 0.881

c) The correlation coefficient and co-variance shows that there is positive association between marks and study time. The correlation coefficient suggest that there is strong positive association between marks and study time.

Step-by-step explanation:

a.

As the mentioned in the given instruction the co-variance is first computed in excel by using only add/Sum, subtract, multiply, divide functions.

Marks y Time spent x y-ybar x-xbar (y-ybar)(x-xbar)

77                    40 5.1         1.3 6.63

63                     42 -8.9            3.3 -29.37

79                     37 7.1            -1.7 -12.07

86                     47 14.1            8.3 117.03

51                    25 -20.9  -13.7 286.33

78                     44 6.1            5.3 32.33

83                      41 11.1            2.3 25.53

90                     48 18.1            9.3 168.33

65                     35 -6.9           -3.7 25.53

47                    28 -24.9 -10.7 266.43

$Covariance=\frac{sum[(y-ybar)(x-xbar)]}{n-1}$

Co-variance=886.7/(10-1)

Co-variance=886.7/9

Co-variance=98.5222

The co-variance computed using excel function COVARIANCE.S(B1:B11,A1:A11) where B1:B11 contains Time x column and A1:A11 contains Marks y column. The resulted co-variance is 98.52222.

b)

The correlation coefficient is computed as

$Correlation coefficient=r=\frac{sum[(y-ybar)(x-xbar)]}{\sqrt{sum[(x-xbar)]^2sum[(y-ybar)]^2} }$

(y-ybar)^2 (x-xbar)^2

26.01        1.69

79.21       10.89

50.41             2.89

198.81       68.89

436.81       187.69

37.21       28.09

123.21        5.29

327.61        86.49

47.61         13.69

620.01         114.49

sum(y-ybar)^2=1946.9

sum(x-xbar)^2=520.1

$Correlation coefficient=r=\frac{886.7}{\sqrt{520.1(1946.9)} }$

$Correlation coefficient=r=\frac{886.7}{\sqrt{1012582.69} }$

$Correlation coefficient=r=\frac{886.7}{1006.2717 }$

$Correlation coefficient=r=0.881$

The correlation coefficient computed using excel function CORREL(A1:A11,B1:B11) where B1:B11 contains Time x column and A1:A11 contains Marks y column. The resulted correlation coefficient is 0.881.

c)

The correlation coefficient and co-variance shows that there is positive association between marks and study time. The correlation coefficient suggest that there is strong positive association between marks and study time. It means that as the study time increases the marks of student also increases and if the study time decreases the marks of student also decreases.

The excel file is attached on which all the related work is done.

Download xlsx