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.