Question 6 10 marks The competitors in the :under 165 age group think the cycling part of the triathlon course was particularly easy compared with previous events and the mean time to complete this part of the triathlon was faster than usual. They claim that the population mean time to complete the cycling part of the triathlon for the under 16 age group is 22.9 minutes. The results for the 'under 16' class of competitors have been extracted from the le summonmwx and saved in a new le underl22B.mwx. (a) ('3) Write down suitable null and alternative hypotheses to test the theory that the population mean time in minutes for under 165 to complete the cycling part of the triathlon is 22.9I minutes. State clearly the meaning of any symbols that you use. Using the data in underl22B.mwx, carry out a one-sample t-test to test the hypotheses that you wrote down in part (a). In your answer, make sure to include the following: a the estimated standard error - the value of the test statistic I the pvalue or the values of CV5 and CV1 - what conclusions can be drawn from the results of this test. Calculate by hand the 95% condence interval for the population mean time takem for under 163 to complete the cycling part of the triathlon based on the t-test. Show your working. Would a 99% condence interval for the population mean time taken for under 165 to complete the cycling part of the triathlon be wider or narrower than the 95% condence interval that you calculated in part (c). C1 C2 C3 C4 C5 C6 C7 C8-T C9-T C10-T START NUMBER SWIM T1 CYCLE T2 RUN TOTAL ELITE HOME CLASS 51 23.44 1.33 22.38 2.27 30.11 79.53 N A Under 16 2 52 22.94 1.24 22.95 2.18 34.49 83.80 N A Under 16 W 53 20.55 0.74 21.23 2.46 27.96 72.94 N H Under 16 4 54 22.22 1.06 25.74 1.81 31.71 82.54 N A Under 16 5 56 25.78 1.12 21.30 2.53 33.89 84.62 N H Under 16 57 20.55 0.91 19.71 1.48 32.09 74.74 N A Under 16 58 22.20 1.22 22.73 1.94 32.33 80.42 N A Under 16 8 59 24.63 1.12 24.91 2.46 31.27 84.39 N A Under 16 9 60 19.81 0.81 17.21 1.52 26.35 65.70 N A Under 16 10 61 18.60 1.11 18.06 1.81 27.25 66.83 N A Under 16 11 62 20.23 0.85 19.34 1.61 28.46 70.49 N A Under 16 12 63 18.58 1.18 15.67 2.22 25.78 63.43 N H Under 16