Question 2: Annual salary (in $1060) of 12 supervisors classied by sex (1 is male and [l is female) are given below: Sex000909111111 Salary 54 49 68 66 62 62 56 65 74 64 68 72 The following model is used to analyze the data set: Salary = [30 + 313.22: + E where 1, . . . ,6", are iid normal with mean f] and variance 0'2. a. Interpret [30 and .31 in the context of this question. b. Is there evidence that the mean salary of male supervisors is higher than the mean salary of female supervisors? c. Let nM be the mean salary of male supervisors and rip be the mean salary of female supervisors. Obtain a 95% condence interval for the difference in mean salary of male supervisors and female supervisors. d. Obtain a 95% joint Bonferroni condence region for nM and #1:. e. Obtain a 95% simulataneous condence region for (g, {31]. Also obtained a 95% joint Bonferroni condence region for {,80, [31). f. Draw the answers obtained in part {e} on the same graph. g. Based on the plot in part {f}, give a point ("5:0 = (g, ,6?) such that 1. g0 is in both condence regions. '2. ,6\" is outside both condence regions. 3. g0 is in the Bonferroni condence region but not the simultaneous condence region. 4. ,8\" is in the simulataneous condence region but not the Bonferroni condence region