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a) Two computers are often compared by running a collection of various \"benchmark\" programs and recording the difference in CPU time required to complete the same program. Six benchmark programs, run on two computers. produced the following table of CPU times (in minutes). Benchmark Program Computer 1 2 3 4 5 6 1 13.44 20.76 12.48 22.32 17.64 25.20 2 11.50 17.20 11.00 18.70 14.60 21.50 (i) Does the data provide sufficient evidence to indicate a difference in mean CPU times required for the two computers to complete a job? Test using or = 0.05. (13 marks) (ii) Based on the fdistribution table. give the most precise estimate for the p- value. (1 mark) (iii) Find a 95% condence interval for the difference in mean CPU time required for the two computers to complete a job. (3 marks) b) Because a new medical procedure has been shown to be effective in the early detection of an illness, a medical screening of the population is preposed. The probability that the test correctly identies someone with the illness as positive is 0.99, and the probability that the test correctly identies someone without the illness as negative is 0.95. The incidence of the illness in the general population is 0.0001. You take the test. and the result is positive. What is the probability that you have the illness? (8 marks)