ii. Based on statistical data, can we infer at the 5% significance level that the mean time to complete this triathlon in a national competition is longer than 54 minutes and 55 seconds? iii. Construct a 90% confidence interval for the population mean time to complete this triathlon in a national competition. (Hint: Express the times in the confidence interval in the hh:mm:ss format.) Explain how the confidence interval supports the results of the hypothesis test. Question 4 The organizers of the Canada Games are interested to know whether there is any association between triathlon medalists and regions. A medalist is an athlete who placed in the top 3. The regions are Western Canada (British Columbia, Alberta, Saskatchewan, Manitoba), Central Canada (Ontario, Quebec), and Atlantic Canada (New Brunswick, Nova Scotia, Prince Edward Island, Newfoundland and Labrador). Consider the following table summarizing the number of triathletes that competed in the Individual Sprint Triathlons in the 2009, 2013, and 2017 Canada Games. Medal ' Non-Medal Western 11 l 56 Central 6 30 61 A Canada Games triathlete is chosen at random. a) What is the probability that they are an Atlantic Canada medalist? b) What is the probability that they won a medal given that they are from Central Canada? c) What is the probability that they are a non-medalist and are not from Atlantic Canada? d) Test at the 5% significance level the claim that medalist is independent from region. (Hint: Use the f test of independence.) Does it appear that certain regions perform better in triathlon events? Question 5 Does the population mean time to complete a triathlon depend on the event? Consider the four triathlon events: Individual Men, Individual Women, Relay Men, and Relay Women. Use the results from the 2009 Individual Sprint and the total team times from 'l'hn 7H1 '2 2|an 9n17 Tnnm Dnlcnl ac camhln Hat-'3