Question 4 (a) A new algorithm is developed to solve a particular type of problem and it is though that this algorithm will solve problems faster than the currently used algorithm. A random sample of 10 problems is selected and they are solved by these two algorithms with the computational time (in seconds) that are given in the following table: Problem 2 3 4 5 6 7 8 9 10 Current 8.05 24.74 28.33 8.45 9,19 25.2 14.05 20.33 4.82 8.54 New 0.71 0.74 0.74 0.77 0.80 0.83 0.82 0.77 0.71 0.72 Test whether the new algorithm is on average, faster than the current one at 1% level of significance. [6 marks ] (b) A factory has 2 machines of the same model that one machine is operated by a well- experienced worker and the other machine is operated by a newly employed worker. Independent samples of number of items produced in an hour during the second week are drawn at random from their records and the statistics are given below. Worker Sample size Mean Variance Well-experienced 12 76.75 29.2955 Newly employed 12 72.3333 26.2424 Can we conclude that the well-experienced worker is more productive than the newly employed worker at 5% level of significance? State your assumptions and /or approximation. [7 marks ]