Question 3 [16 marks] The human resource manager at a car dealership wants to know if the ages of its employees are related to the department that they work in. Data was compiled and tabulated in a 2-way contingency table. The employees were classified according to their age and department. Expected counts are printed below observed counts Sales Accounts Marketing Repairs Total 20-29 8 10 27 43 88 17.74 26.20 23. 62 30-39 29 26 38 22 23. 18 26.72 34 .24 30.86 40-49 33 32 72 82 219 44 . 15 50 .88 65.20 58.77 50-59 81 106 86 54 327 65.92 75.97 97.36 87. 75 Total 151 223 201 749 Chi-sq - 5.348 + 0. 024 + 15. 912 + 1. 459 + 0. 019 + 0. 413 + 2.544 + 2.816 + 7.003 + 0.709 + 9.182 + 3. 448 + 11.875 + 1.325 + 12.983 - 80.395 OF - +*+*#, P-Value = +4+4+ No cells with expected counts less than 5. a) Name the random variables present in the table above. [2] b) Carefully define the null and alternative hypotheses of the Chi Square test underlying the generation of the above table. [2] c) Fill in the gaps marked by "$ $1 1$68 189481 and (8]