west A l - [ Page view | A Read aloud | (T) Add text Question 2 10 marks The file summer.mwx can be used to produce a contingency table giving the count of all competitors grouped by class and home or away status. This contingency table is shown in Table 1. A copy of this contingency table can be found in the file contingency22B.mwx. Using the counts in Table 1, the expected values in each category have been calculated and are shown in Table 2. Table 1 Number of competitors Table 2 Expected values Class Away Home Class Away Home Under 16 3 Under 16 6.27 5.73 16 to 29 20 25 16 to 29 23.53 21.47 30 to 39 20 12 30 to 39 16.73 15.27 40 to 49 40 40 to 49 34.50 31.50 50 to 59 26 49 50 to 59 39.21 35.79 60 and over 21 60 and over 28.23 25.77 Elite 38 7 Elite 23 53 21.47 (a) What is the probability that a randomly selected competitor is aged under 30 (ic. that they are in either the "under 16' class or the '16 to 20' class)? (b) Given that a randomly selected competitor is an 'away' competitor, what is the probability that they are aged under 30 (Le. that they are in either the "under 16" class or the '16 to 20' class)? (c) Is the event that a randomly selected competitor is aged under 30 statistically independent from the event that a randomly selected competitor is an away competitor? Justify your answer. Suppose a researcher is interested in ining this sample to answer the following question: O U O hp