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Course: STA416 - Applied Probability and Statistics

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QUESTION 2 a) A genetic expert investigated the nature of the relationship between intelligence score and social dominance in albino mice. A random sample of six albino mice are chosen and the data collected are shown below. Intelligence score Social dominance score 45 63.7 26 0.1 20 15.6 40 101.2 36 25.4 23 1.8 Source: "A Study of the Relationship between Social Dominance and Intelligence in Albino Mice", unpublished research report, 1975. Calculate the Spearman's rank correlation coefficient between the intelligence score and social dominance in albino mice and interpret the value. (5 marks)b) The efficiency of a new computer program will depend on the size of the incoming data. Efficiency will be measured by the number of process requests per hour. The table below shows the results of applying the program to the data sets of different sizes. Data size (gigabytes) Process requests 6.5 292 6.9 329 7.8 252 8.4 378 8.8 392 9.2 410 6.7 198 6.9 227 7.5 277 7.9 297 8.7 364 9.2 375 6.5 167 7.0 2257.2 247 7.6 268 8.7 288 9.2 342 Scatter plot between Data Size (gigabytes) and Process Requests 500 400 300 Process requests 200 100 6 6.5 7 7.5 8 8.5 9 9.5 Data size i) Given the scatter plot, describe the relationship between data process requests and data size. (1 mark) i) Given Ex = 140.7; Zy = 5328; Ex? = 1116.01; Zy = 1661704; Exy = 42591.7 and the Pearson's Product Moment Correlation Coefficient, r = 0.8066. Determine the estimated regression equation and interpret the slope in the context of the problem. (5 marks)iii) Estimate the amount of process requests if the data size is 9.0 gigabytes. (2 marks)