Question

Question 5 [20 marks]
a. A shop owner wanted to find out if increasing the volume of music played during
peak shopping hours influenced the sales volumes. After collecting a series of data
over a specific period and subsequent statistical analysis, it was established that the
correlation coefficient of determinant (r2) was 0.80. What is your interpretation of the
relationship between the two variables?
b. An employer interviews students from University of Botswana (UB) and University
of South Africa (UNISA). She learns that the colleges are similar and that both grade
graduates on a 4.0 scale. The mean grade point average at UB is 2.62 with standard
deviation (SD) of 0.50, whereas as the mean grade point average at UNISA is 3.24
with SD of 0.40. The employer suggests the grades at UNISA are inflated. Thabo, a
graduate from UB has a grade point average of 3.62, while Sandra from UNISA has a
grade point average of 3.64. Assume that both students took the same courses. The
employer wants to adjust the grades for the grading practices of the two colleges.
Using your knowledge of measures of dispersion/variation, test the employer’s
assumption.

Answer 1

a)

Correlation coefficient of determination signifies how data points fall within the results of the line/curve formed by the regression equation. If the coefficient is 0.80, then 80% of the points should lie on the regression line. Values of 1 or 0 would indicate the regression line represents all or none of the data, respectively. A higher coefficient is an indicator of a better goodness of fit for the observations.We can interpret that increasing the volume of music played during peak hours has highly and positively influenced the sales volume.

b) The coefficient of variation is a statistic that is the ratio of the standard deviation to the mean expressed in percentage and is denoted CV.When the value of the coefficient of variation is lower, it means the data has less variability and high stability.

First Lets calculate the C.V for University of Botswana (C.V_bot)

C.V_bot = 19.08%

Now for University of South Africa,(C.V_SA)

C.V_SA = 12.34%

Based on the values of C.V, we can infer that the grades at the University of South Africa have less variability compared to that of the University of Botswana.This contradicts the assumption of the employer about UNISA are inflated.