a) For each of the four events, construct a separate histogram of total times. b) Perform at the 5% significance level the one-way ANOVA test to compare the population mean times for each of the four events. Should we reject or not reject the claim that there is no difference in population means between each event? c) Closely examine the histograms in part a). Consider the requirements for an ANOVA test and determine if the result obtained in part b) is in fact valid. Justify your choice. Question 6 Athletes complete the components of a triathlon in the order of swim, bike, and run. Which pair of components have a linear relationship that can be used for predictions? Investigate the following pairs of components: a Bike (dependent) vs. Swim (independent) - Run (dependent) vs. Swim (independent) a Run (dependent) vs. Bike (independent) Consider the female triathletes who competed in the Canada Games as a sample of all female triathletes. Part A: Women Sprint Triathlon Consider Sprint results from the 2009. 2013. and 2017 Women Individual Triathlon. iv. For each pair of components, a. construct a separate scatter plot, b. find the corresponding correlation coefficient, and c. find the corresponding coefficient of determination. v. Which pair of components has the strongest linear relationship in the sprint triathlon? Find the equation of the trend line for this pair and add it to the corresponding scatter plot. Part B: Women Super Sprint Triathlon Consider Super Sprint results from the 2009 and 2013 Women Relay Triathlon. (Hint: The athlete's individual performance in a Team Relay is their Super Sprint data.) i. The pair of components that has the strongest linear relationship in the super sprint triathlon is between swim (independent) and run (dependent). Find the equation of this trend line and add it to the scatter plot. ii. Compare the strongest linear relationship in the sprint triathlon to the strongest linear relationship in a super sprint triathlon. iii. Estimate the expected run time for a female super sprint triathlete who finished the swim component in 4 and a half minutes. (Hint: Express the run time in mm:ss format.)