NUM 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 SALARY $44,000 $51,000 $44,000 $43,000 $47,000 $42,000 $49,000 $50,000 $48,000 $46,000 $52,000 $45,000 $53,000 $52,000 $44,000 $49,000 $40,000 $46,000 $47,000 $46,000 $50,000 $43,000 $52,000 $47,000 $46,000 $47,000 $57,000 $59,000 $52,000 $53,000 $52,000 $56,000 $56,000 $54,000 $59,000 $66,000 $64,000 $40,000 $47,000 $56,000 $55,000 $54,000 $60,000 $54,000 $61,000 $54,000 $55,000 $54,000 $55,000 $56,000 $44,000 $52,000 $62,000 $44,000 $60,000 $50,000 $51,000 $42,000 $53,000 $44,000 $52,000 $54,000 $54,000 $41,000 $49,000 $52,000 $46,000 $42,000 $63,000 $48,000 $48,000 $55,000 $48,000 $51,000 $52,000 $48,000 AGE 26 39 35 40 29 25 28 33 62 32 34 38 37 58 33 27 30 37 45 30 36 29 45 34 24 27 61 49 40 34 35 44 38 43 47 42 47 25 31 41 27 33 51 36 37 63 38 45 54 58 41 52 42 54 59 44 32 64 47 37 46 35 56 39 51 38 30 26 42 35 57 53 32 45 26 31 PRIOR 1 1 0 7 0 0 0 2 0 0 2 8 0 6 0 0 0 9 6 3 2 3 0 4 1 1 6 0 6 7 4 0 0 8 2 0 0 2 4 0 2 1 0 0 1 0 1 0 3 0 0 10 0 0 3 10 0 0 1 0 0 8 0 0 0 8 3 0 1 4 4 8 4 5 1 9 EDUC 4 1 1 2 4 3 3 3 1 3 4 2 2 2 3 3 3 2 4 2 3 2 1 2 3 4 2 1 1 2 1 1 2 4 2 2 1 3 2 1 4 3 1 5 3 3 3 1 1 2 1 4 1 2 1 1 2 1 3 3 2 2 1 1 3 2 2 3 5 3 2 1 3 1 4 1 COMP 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 GRADE 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 EXPERI 4 15 13 9 4 4 5 9 5 10 10 9 10 11 5 4 7 9 6 5 5 4 6 4 4 4 17 14 13 5 8 12 14 4 19 15 20 4 3 12 4 6 16 8 13 14 13 19 18 10 11 6 16 3 4 5 8 9 16 10 17 5 9 10 19 4 7 5 6 5 8 12 6 18 4 6 GENDER 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 0 1 CITIZEN 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 LOCATION 2 3 1 2 1 3 3 3 2 4 2 2 3 3 2 3 2 3 3 3 3 4 3 4 1 2 3 4 4 5 5 4 2 4 4 5 2 3 4 4 5 2 3 3 3 4 3 4 4 4 3 2 4 4 5 5 5 2 4 4 4 5 5 2 5 2 2 3 1 1 2 4 1 3 1 2 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 $49,000 $58,000 $48,000 $63,000 $47,000 $59,000 $52,000 $54,000 $66,000 $44,000 $55,000 $61,000 $44,000 $57,000 $67,000 $44,000 $50,000 $55,000 $59,000 $58,000 $41,000 $45,000 $47,000 $44,000 $59,000 $72,000 $61,000 $47,000 $54,000 $47,000 $52,000 $47,000 $58,000 $56,000 $64,000 $51,000 $62,000 $55,000 $51,000 $54,000 $49,000 $66,000 $54,000 $54,000 $59,000 $66,000 $51,000 $58,000 $54,000 $53,000 $50,000 $49,000 $52,000 $54,000 $64,000 $63,000 $51,000 $51,000 $62,000 $49,000 $59,000 $63,000 $58,000 $56,000 $59,000 $65,000 $55,000 $61,000 $56,000 $60,000 $50,000 $60,000 $65,000 $62,000 $70,000 $65,000 $66,000 51 48 36 43 46 36 23 58 40 30 35 30 32 53 34 50 35 27 29 35 47 52 27 34 27 34 29 28 44 36 39 60 44 49 33 32 29 36 37 44 33 59 44 37 48 27 26 39 41 29 59 29 27 37 30 34 35 51 33 27 36 34 47 52 43 31 62 46 61 44 54 39 40 45 36 40 33 0 3 0 0 10 0 0 0 0 0 0 4 9 18 5 0 7 1 0 2 1 0 2 0 2 0 0 0 0 3 0 0 5 5 3 0 2 0 12 0 5 4 7 8 6 0 0 0 0 0 0 4 2 0 0 5 2 6 1 0 0 5 0 0 6 0 10 1 9 5 2 1 5 5 0 3 3 1 5 3 2 2 5 4 2 5 3 3 5 1 2 5 1 2 5 5 5 1 1 3 3 4 5 4 3 1 3 1 2 3 2 5 3 5 3 3 2 3 4 3 3 5 5 3 4 3 3 2 2 3 2 5 2 3 2 5 3 5 5 3 1 1 5 2 5 3 4 1 3 5 4 5 4 5 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 10 4 5 17 10 4 5 9 9 7 12 5 4 13 4 9 7 4 5 4 16 16 4 13 3 9 6 6 12 5 10 15 5 16 8 6 8 8 5 11 6 12 10 5 6 5 6 7 7 6 10 6 4 13 5 8 9 13 4 5 4 4 9 22 17 6 26 7 22 7 26 14 7 7 8 9 6 1 1 0 1 1 0 0 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 0 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 1 4 4 5 4 3 4 2 1 4 2 3 4 3 2 1 1 3 4 5 5 2 2 3 3 4 5 4 3 1 1 3 3 2 2 4 5 4 2 1 3 3 5 3 4 5 4 3 3 3 3 3 2 3 3 4 4 1 2 1 3 3 1 3 4 4 5 3 4 3 2 3 3 1 3 4 4 4 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 $72,000 $75,000 $80,000 $85,000 $85,000 $93,000 $88,000 $87,000 $78,000 $89,000 $84,000 $85,000 $81,000 $88,000 $87,000 $86,000 $80,000 $90,000 $84,000 $84,000 $82,000 $94,000 $83,000 $82,000 $85,000 $88,000 $85,000 $82,000 $80,000 $69,000 $94,000 $85,000 $88,000 $98,000 $75,000 $83,000 $86,000 $101,000 $87,000 $87,000 $80,000 $90,000 $93,000 $96,000 $98,000 $94,000 $92,000 $100,000 $96,000 $90,000 $99,000 $95,000 $98,000 $112,000 $104,000 $113,000 $114,000 $118,000 $150,000 $130,000 $128,000 $147,000 $160,000 $187,000 $198,000 $212,000 $210,000 $203,000 $634,000 33 30 38 31 32 38 35 30 50 30 32 32 47 44 27 56 53 50 60 48 44 41 42 39 39 40 49 53 38 40 34 37 31 32 41 46 38 34 35 50 34 32 49 40 37 46 44 36 39 37 41 55 57 50 41 59 52 45 56 57 54 65 66 61 61 62 60 63 68 3 1 3 0 4 3 1 1 9 0 0 2 4 0 0 0 4 12 8 0 4 0 0 4 0 1 0 1 0 2 0 0 0 0 10 4 2 0 5 5 2 0 4 2 2 2 0 1 0 6 7 3 1 0 0 4 0 0 1 0 0 0 0 0 0 0 0 0 0 5 5 5 5 5 5 4 5 4 5 5 5 2 3 5 4 3 5 3 3 3 5 3 4 5 3 3 2 3 2 5 5 5 5 5 3 5 5 3 5 5 5 5 5 5 5 4 5 5 5 5 3 5 5 4 5 5 5 5 5 4 4 5 4 5 5 5 5 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 CEO 6 5 7 7 6 8 11 6 14 7 8 7 16 18 5 24 6 4 20 27 7 16 17 13 10 15 17 17 12 14 8 9 9 8 7 18 9 9 9 17 7 8 9 13 10 13 17 12 14 10 17 25 18 15 14 20 13 21 21 23 22 31 40 35 37 33 36 34 41 0 0 0 0 1 1 1 0 1 0 1 0 1 1 0 0 0 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 1 1 1 1 1 1 1 1 3 3 3 2 3 4 4 2 2 2 3 2 3 3 5 3 3 2 3 3 3 3 5 5 5 4 3 3 4 4 5 3 3 5 2 3 4 5 2 3 4 5 4 4 5 4 4 5 5 5 4 3 3 4 4 4 4 5 4 3 3 4 4 5 5 5 5 5 5 MGSC2301 GROUP PROJECT #3 (Conf Int/Hypo Test) Spring, 2016 General Instructions/Information: Project #3 is due on Monday, March 21. Project #3 will be scored on a 50-point scale. You are encouraged, but not required, to work with one or two partners on Project #3. If you do choose to work as a group of 2 or 3, then only one paper need be submitted and all members of the group will receive the same grade. Please record all answers on the Yellow Sheet which accompanies this assignment; 4-place accuracy is sufficient for all answers. For written answers, assume your reader is intelligent, but not a statistician. MGSC2301 PROJECT #3 (Conf Int/Hypo Test) Page 1 This project again utilizes the data set for the Bank and Trust Company (B&T); the random sample of 222 employees and data recorded for several variables: Annual salary earned by the employee; The age of the employee; The years of experience in the banking industry held by the employee prior to joining B&T; The education level of the employee; The extent to which the employee uses a computer; The grade classification within B&T held by the employee; The years of experience at B&T; The gender of the employee; The citizenship of the employee; and A location adjustor for salary using a 1-5 scale. Assume that you still work for Ms. Deanna V. Ashun (aka \"Dee\") and that the lawsuit alleging gender bias has been resolved in favor of B&T. But more work remains, and Ms. Ashun has asked you to complete several tabulations and calculations, excluding the CEO from all calculations. Note: Assume normality!!! ************************************************ #1: (a) What is the point estimate for the average annual salary paid to B&T employees in each of the six grades? Please round your answers to the nearest whole dollar. (12 points) (b) For the Vice Presidents (GRADE 6) only, find the 95% Confidence Interval for the average annual salary. (2 points) (c) Ms. Ashun's boss, Mr. Samuel Pellsize, is an intelligent man, but has limited statistical training. In a maximum of two sentences, provide a managerial interpretation of your numeric result from part (1b); this interpretation will be read by Mr. Pellsize. (2 points) (d) For part (b), did you use the Finite Population Correction Factor? Why or why not? (4 points) MGSC2301 PROJECT #3(Conf Int/Hypo Test) Page 2 Mr. Pellsize is glad that the gender bias lawsuit has been resolved, but does still wonder about B&T's promotion practices. For example, he is aware that in the sample being used, 14 out of 15 vice presidents are male. Since many of the vice presidents are promoted from within, this leads to a concern that B&T might not have an adequate pool of female senior officers (GRADE 5). So he wonders if B&T exhibits some form of gender bias in terms of the promotion of branch managers/junior officers (GRADE 4) to senior officers (GRADE 5). Note: this is often referred to a glass ceiling for women. Mr. Pellsize and Ms. Ashun decide to be pro-active and start an investigation. #2: Ms. Ashun quickly asks you for the following calculations: (a) What proportion of the branch managers/junior officers (GRADE 4) is female? (2 points) (b) What proportion of the senior officers (GRADE 5) is female? (2 points) (c) Find a 99% confidence interval for the proportion of females in GRADE 4. (2 points) (d) Find a 95% confidence interval for the proportion of females in GRADE 5. (2 points) (e) Assuming your reader is Mr. Pellsize, explain the numerical values found in part (2c & 2d) above - using a maximum of two sentences. (2 points) PROJECT #3 (Conf Int/Hypo Test) MGSC2301 Page 3 Still somewhat concerned, Ms. Ashun asks you to continue to focus on the B&T employees in GRADES 4 and 5. She does some research - investigating other North American banks the size of B&T. She finds that on average, branch managers in other banks get paid an average of 80,000/year and that senior officers get paid an average of $90,000/year. She wonders if B&T pays comparable salaries. #3: (a) Find the average salary for the females in GRADE 4. Please round your answer to the nearest whole dollar. (2 points) (b) If: Females4 = average salary for all B&T females in GRADE 4 Test the following hypothesis using =0.01(Assume normality): H0: Ha: vs Females4 $80,000 Females4 > $80,000 Specify if you reject or fail to reject H0. In the context of the problem specify your final conclusion in words. (3 points) (c) Find the average salary for the males in GRADE 4. Please round your answer to the nearest whole dollar. (2 points) (d) If: Males4 = average salary for all B&T males in GRADE 4 Test the following hypothesis using =0.01 (Assume normality): vs H0: Ha: Males4 $80,000 Males4 > $80,000 Specify if you reject or fail to reject H0. In the context of the problem specify your final conclusion in words. (3 points) PROJECT #3 (Conf Int/Hypo Test) MGSC2301 (e) Find the average salary for the females in GRADE 5. Please round your answer to the nearest whole dollar. (2 points) (f) If: Females5 = average salary for all B&T females in GRADE 5 Test the following hypothesis using =0.05 (Assume normality): H0: Ha: vs females5 $90,000 females5 > $90,000 Specify if you reject or fail to reject H0. In the context of the problem specify your final conclusion in words. (3 points) (g) Find the average salary for the males in GRADE 5. Please round your answer to the nearest whole dollar. (2 points) (h) If: Males5 = average salary for all B&T males in GRADE 5 Test the following hypothesis using =0.05 (Assume normality): vs H0: Ha: Males5 $90,000 Males5 > $90,000 Specify if you reject or fail to reject H0. In the context of the problem specify your final conclusion in words. (3 points) Page 4 MGSC2301 YELLOW SHEET FOR: NAME(S): PROJECT #3 Spring, 2016 _____________________________________ _____________________________________ _____________________________________ SCORE (out of 50): ______________________ *********************************************** #1: (a) Point estimates for average annual salary by grade, rounded to nearest whole dollar: Grade of B&T Employee Estimated Annual Salary 1 2 $ 3 $ 4 $ 5 $ 6 (b) $ $ 95% C.I. for average annual salary of GRADE 6 Employees = [ $ _____________ , $ ______________ ] MGSC2301 (c) YELLOW SHEET FOR: Managerial interpretation of (1b): PROJECT #3 Page 2 (to be read by Mr. Pellsize) _____________________________________________________________ ____________________________________________________________ _____________________________________________________________ (d) Finite Population Correction Factor was used? Rationale: YES NO ______________________________________________ ______________________________________________ ______________________________________________ #2: (a) pFEMALE in GRADE 4 = ____________________________ (b) pFEMALE in GRADE 5 = ____________________________ (c) 99% C.I. for pFEMALE in GRADE 4 = ( _______________ , _______________ ) (d) 95% C.I. for pFEMALE in GRADE 5 = ( _______________ , _______________ (e) Explanation of 99% C. I. for pFEMALE in GRADE 4: ____________________________________________________________ ____________________________________________________________ Explanation of 95% C. I. for pFEMALE in GRADE 5:___________________ ____________________________________________________________ MGSC2301 #3: (a) (b) YELLOW SHEET FOR: PROJECT #3 Average annual salary for females in GRADE 4: Hypothesis test ( = 0.01): vs Conclusion: H0: Ha: Fail to reject H0 Page 3 _ XFemales4 = ____________ Females4 $80,000 Females4 > $80,000 Reject H0 Conclusion in context of problem: I/we are 99% confident that on average, female branch managers at B&T earn annual salaries in excess of $80,000. There is no enough evidence to conclude that female branch managers at B&T earn average annual salaries in excess of $80,000. (c) I/we are 99% confident that on average, female branch managers at B&T earn annual salaries of $80,000 or less. _ Average annual salary for males in GRADE 4: XMales4 = ____________ (d) Hypothesis test ( = 0.01): vs Conclusion: Fail to reject H0 H0: Ha: Males4 $80,000 Males4 > $80,000 Reject H0 Conclusion in context of problem: I/we are 99% confident that on average, male branch managers at B&T earn annual salaries in excess of $80,000. There is no enough evidence to conclude that male branch managers at B&T earn average annual salaries in excess of $80,000. I/we are 99% confident that on average, male branch managers at B&T earn annual salaries of $80,000 or less. MGSC2301 YELLOW SHEET FOR: (e) Average annual salary for females in GRADE 5: (f) Hypothesis test ( = 0.05): vs Conclusion: H0: Ha: Fail to reject H0 PROJECT #3 Page 4 _ XFemales5 = ____________ Females5 $90,000 Females5 > $90,000 Reject H0 Conclusion in context of problem: I/we are 95% confident that on average, female senior officers at B&T earn annual salaries in excess of $90,000. There is no enough evidence to conclude that female senior officers at B&T earn average annual salaries in excess of $90,000. (g) I/we are 95% confident that on average, female senior officers at B&T earn annual salaries of $90,000 or less. _ Average annual salary for males in GRADE 5: XMales5 = ____________ (h) Hypothesis test ( = 0.05): vs Conclusion: Fail to reject H0 H0: Ha: Males5 $90,000 Males5 > $90,000 Reject H0 Conclusion in context of problem: I/we are 95% confident that on average, male senior officers at B&T earn annual salaries in excess of $90,000. There is no enough evidence to conclude that male senior officers at B&T earn average annual salaries in excess of $90,000. I/we are 95% confident that on average, male senior officers at B&T earn annual salaries of $90,000 or less. MGSC2301 DATA BASE FOR GROUP PROJECTS Spring, 2016 The data set includes observations for 222 employees from Bank & Trust (B&T). B&T operates branches throughout North America and employs approximately 15,000 people. The data shown here were collected randomly from this population of 15,000; it is of interest to note that the CEO just happens to be included in this sample. The variables shown in the data base are: Column A: Column B: Column C: Column D: Column E: Column F: Column G: Column H: Column I: Column J: Column K: NUM SALARY The observation number (note sorting by grade) The annual salary of the employee as of Jan 1 (rounded to the nearest $1000) AGE The age of the employee as of Jan 1 (nearest whole year) PRIOR The employee's years of experience in the banking industry prior to joining B&T (nearest whole year) EDUC The education level of the employee on a 1-5 scale: 1: Did not finish high school 2. HS diploma or equivalent 3. Has some college but no degree 4. Has undergraduate degree 5. Has graduate degree COMP 0/1 variable to indicate extent of daily computer usage 0: Uses computer only for record-keeping 1: Uses computer extensively for analysis GRADE 1-6 scale to indicate job classification at B&T 1: Junior teller/secretary 2: Senior teller/administrative assistant 3. Analyst/investment counselor 4. Branch Manager/Junior Officer 5. Senior Officer 6. Vice President CEO is not ranked on this 1-6 scale EXPERI Years of experience at B&T as of Jan 1 (nearest whole year) GENDER 0: Male 1: Female CITIZEN: The citizenship held by the employee: 1: United States 2: Canada 3. Mexico 4. Other LOCATION: A factor to incorporate the cost of living where the branch is located 1: Lowest (e.g., Des. Moines) 5: Highest (e.g., New York City)