Question 6 (10 marks). Two rival software companies, Company A and Company B, both claim they have created the world's best video compression algorithm. To decide which company's algorithm is better, an independent body decides to run some tests. The algorithms were used to compress 4K movie files, and the ratio of the compressed file size to the original size of the file was recorded. A smaller ratio is considered superior. Assume that differences in the time taken to compress files, and differences in the quality of the compressed files, are negligible between the two algorithms. Company A's algorithm, which we will call algorithm A, was tested on n1 = 30 randomly chosen 4K movies. The average ratio of compressed file sizes to the original sizes was 0.3, with a sample standard deviation of 0.086 Company B's algorithm, which we will call algorithm B, was tested on n2 = 33 randomly chosen 4K movies. The average ratio of compressed file sizes to the original sizes was 0.2, with a sample standard deviation of 0.092. Let uj and 2 denote the true mean ratio of compressed file size to original file size, for algorithm A and algorithm B, respectively. For the two-sample t-test, the degrees of freedom is approximately df = 61 and you should use this value for the following questions. a. (1 mark) What is the estimated mean difference in the ratios of the compressed file sizes produced by the two algorithms, compared to the original file sizes? b. (3 marks) Calculate the standard error for this estimated mean difference. c. (3 marks) Calculate a 95% confidence interval for the difference in the two means. You may use the fact that to1 = 2.0 d. (3 marks) Assuming that this ratio is the only way in which differences between the two algorithms are measured, does your confidence interval suggest that one algorithm is better than the other? If so, explain why, and indicate which algorithm is better, and by how much. If not, explain why not. When performing calculations in this question, give at least 3 decimal places of accuracy. Show all working. Include your answers in the document you submit at the end of the exam