Type Age: - 15-24 years 25-54 years 55 and over Total: of work I Full-time 5426 42019 10588.4 58033.4 employee Part-time 5355.8 4926 2528.6 12,810.4 employee Total 10781.8 46945 13117 70,843.8 Assuming that a single employee recently hired is randomly selected from the sample data: (a) What is the probability that the employee is from the 15 - 24 age group given that the work is part-time? (b) What is the probability that the work is part-time and the employee is from the 15 - 24 age group? (c) What is the probability that the work is part-time given that the employee is from the 15 - 24 age group? (d) Is the employee's full-time work status independent from their 15 - 24 age group? (e) Test, at the 5% significance level, the claim: the type of work (full/part-time) is independent from the age category. Should Ho be rejected at the 5% significance level? (Hint: use the x test of independence). Give an explanation for your conclusion