A study was commissioned to investigate the characteristics of employees at a major business. Data was collected on 60 employees and the following variables recorded. Column 1 Gender What is your gender? (1 = Male, 0 = Female) Column 2 Age How old are you? Column 3 Salary What is your yearly salary (before Tax)? Column 4 Overtime How much overtime do you work each week? Column 5 Job Type What department do you work in? (1 = Purchasing, 2 = Marketing/Human Resource, 3 = Accounting) QUESTION 1 (7 marks) The company has been accused of gender inequality. Test, at the 5% level of significance, whether the average salary of males is greater than the average salary of females [You may assume that the unknown population standard deviations for male and female salaries are equal] QUESTION 2 (6 marks) Test, at the 5% level of significance, whether Job Type of an employee is related to the employee's gender? QUESTION 3 (7 marks) Can we conclude, at a 5% level of significance, that a linear relationship exists between the employee's Salary (y) and employee's Age (x)?1 Gender Age Salary Overtime Job 2 0 19 29000 11 0 36 49000 4 2 A 27 56000 10 1 5 22 28000 11 2 6 18 45000 12 1 7 20 33000 5 8 33 40000 2 9 26 56000 5 10 29 47000 11 37 58000 12 27 41000 4 13 39 60000 H H N N N N N N N A N N NW 14 36 49000 0 15 23 58000 21 16 26 41000 12 17 18 66000 18 53 71000 0 19 27 52000 10 20 39 71000 2 2 21 34 55000 0 3 22 1 38 50000 4 1 23 1 45 67000 1 3 24 40 47000 6 2 25 34 56000 2 26 1 36 56000 2 1 27 0 18 39000 12 28 52 80000 2 3 29 36 55000 2 3 30 32 50000 2 3 31 23 40000 11 3 32 G G O G GH 36 46000 2 2 33 31 48000 4 1 34 46 48000 2 3 35 27 32000 10 3 36 29 40000 4 2 37 47 50000 3 38 25 33000 8 139 0 40 63000 2 40 1 36 65000 5 3 41 0 37 56000 2 42 1 44 68000 w N NN 43 0 25 36000 17 44 0 24 45000 45 0 48 75000 6 1 46 1 42 40000 6 3 47 1 24 51000 12 3 48 0 30 43000 1 49 0 31 52000 2 50 1 32 63000 3 51 1 24 42000 0 52 0 39 74000 1 53 0 50 52000 3 54 0 22 29000 10 I N N O N N N G N P N NN 55 0 45 60000 56 1 45 60000 3 57 1 54 69000 2 58 0 36 66000 9 59 1 37 46000 2 60 0 23 29000 11 61 1 35 54000 1 2