(20 points) The following table comes from a study by the chemist and Nobel Laureate Linus Pauling. It gives data regarding incidence of cold among 279 French skiers who were randomized to two groups. One group was given Vitamin C, whereas the other group was given a Placebo. The table below shows the number of skiers who got the colds in the groups. Observed Frequencies Cold Vitamin C yes No Total yes 17 122 139 no 3l 109 140 Total 48 231 279 (@) (b) () (d) (5 points) Calculate the sample proportion of skiers that got colds in the Vitamin C group. Then calculate the sample proportion of skiers that got colds in the Placebo group. What is the different between the sample proportions? (5 points) Construct a 90% confidence interval for the difference between true proportions of skiers that got colds in the two groups. (5 points) Calculate the expected frequencies under the hypothesis that the two variables, "Vitamin C (yeso)" and "Cold (yeso)", are independent. (5 points) Was there an association between the two variables "Vitamin C (yeso)" and "Cold (yeso)"? Calculate the test statistic for the 2 (Chi-square) test of independence. What is your conclusion at significance level 0.05