7) It has been claimed that in competitive sports there might be some advantage for teams wearing blue uniforms. You want to test this with the sport of competitive swimming. You conduct a study using 35 separate races where 3 competitive swimmers are chosen at random and assigned either a blue, red, or green swimsuit for each race. The swimmer wearing a blue swimsuit won in 18 of the 36 races. (a) What is the value of the sample statistic and what symbol should be used to represent it? (b) Describe the parameter of interest in the context of the study and state which symbol should be used to represent it. (c) What is a plausible value for the parameter if wearing a blue swimsuit does not provide a competitive advantage? (d) Does the sample statistic prove that wearing blue provides a competitive advantage? Explain using complete sentences. (e) Suppose you wanted to Create a Distribution of Simulated Sample Statistics for One Proportion with 300 simulated sample statistics. The applet and a distribution of simulated sample statistics is shown below. Fill in the blanks that were used to generate the distribution. Describe process: Summary Stats Probability of success (TT): Sample size (n): Number of samples: 2 Draw Samples As extreme as [7] Count t 2 OR O 0.09 0.17 0.26 0.34 0.43 0.51 0.60 Proportion of successes (f) (Fill in the blanks) The distribution above has a mean of 0.329 and a standard deviation of 0.081. According to the 2 Standard Deviations Rule, when sampling 35 competitive swimming races where swimsuit color does not provide a competitive advantage, it would be unusual for the wearer of the blue swimsuit to win less than % or more than % of their races. [g) Use the distribution of 300 simulated sample statistics to identify the proportion of statistics that are at least as extreme as the observed statistic. Use that value to complete the following statement: Assuming blue swimsuits do not provide a competitive advantage in a swimming race, the probability of the blue swimmer winning at least 18 out of the 36 races is This means we have evidence to suggest our sample statistic is _ (expected/unusual)