The le winter.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 le contingeneymlwx. Using the counts in Table 11 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 lClass Away Home Under 15 9 3 Under lti 3.2? 5.73 15 to 29 21] 23 13 to 29 24.94 21.95 39 to 39 21] 12 39 to 39 13.72 15.23 49 to 49 25 41 49 to 49 35.91 31.99 59 to 59 25 49 59 to 59 39.19 35.31 ll and over 34 21 69 and over 23.74 26.26 Ellte 39 T Ellte 24.04 21.95 {a} What is the probability that a randomly selected competitor is aged ll or over (Le. that they are in either the '59 to 59" class or the \"fill and over' class}? {b} Given that a randomly selected competitor is a 'bome' competitor. what is the probability that they are aged 59 or over [i.e. that they are in either the '59 to 59' class or the '59 and over' class}? Ic} Is the event that a randomly selected competitor is aged 51] or over statistically independent from the event that a randomly selected competitor is a home competitor? Justify your answer Suppose a researcher is interested in using this sample to answer the following question: Is the distribution of competitors across the dierent classes the some for home competitors and outcry competitors? {d} Write down suitable null and alternative hypotheses. {e} Explain why it is valid to use the X2 test for contingency tables in this case. If} Using llp'linitab1 or otherwise. carry out the x2 test for contingency tables and interpret the results. You should explicitly state: I The value of the test statistic I The degrees of freedom I The p-value or the values ofUV and CV1 I Your conclusion from the test [I] [I] [I] [2] [I] [4]