Library Home Students Staff - Question 6 Question 6 (8 marks). Not yet answered Suppose you had two candidate algorithms, algorithm A and algorithm B, designed to perform analysis on large data sets. Marked out of You wish to determine which of the two algorithms, if any, has the fastest average running time on large data sets. Let u A and AB denote the true mean running time for algorithm A and B, respectively, and then let ud = MA - AB Assume that the differences are normally distributed. Flag question To determine the best algorithm, you conduct a paired two-sample t-test by running each algorithm on the same collection of n =.12 different data sets. Some results are summarised in the table below (where a is the sample mean and s is the sample standard deviation. I A SA SB Sd 73.33 24.98 82.22 25.78 -8.89 4.46 The times are measured in minutes. a. (2 mark) Calculate the standard error for this estimated mean difference. b. (1 marks) What is the degrees of freedom for this t-test? c. (2 marks) Calculate a 95% confidence interval for the difference in the two means. You may use the fact that taf,0.975 = 2.201 for the suitable degrees of freedom df. d. (3 marks) Does your confidence interval suggest that one algorithm performs better than the other? If so, explain why. and indicate which algorithm is better, and by how much. If not, explain why not. Show all working. Give your answers to at least 3 decimal places. Include your answers in the document you submit at the end of the exam, ENG 4:33 PM 31/10/2022