Is there a significant difference, at 5% level of significance, in the average evaluation scores of employees of different job types? The type of job contained in a variable called "JOB", type where a "1" indicates clerical and technical staff, a "2" indicates skilled employees, a "3" indicates supervisory positions, and a "4" indicates management positions.

1. State the null and alternative hypotheses. (5 points)

1. Calculate the test statistic. (5 points)

1. Find the critical value or the p-value. (5 points)

1. State your decision and conclusion in the context of the problem. (5 points)

SCORE	LAG	EMP@EOY	POS@EOY	DEPT	GRADE	EDUC	EMP@E..S@EVAL	TYPE	JOB	HERE
184	-7	7.289999962	7.289999962	40	8	13	7.119999886	7.119999886	1	2	1
155	9	2.920000076	2.119999886	55	13	13	1.820000052	1.019999981	1	4	1
132	21	0.769999981	0.769999981	55	13	16	0.310000002	0.310000002	0	4	1
118	-7	0.800000012	0.800000012	55	4	13	0.230000004	0.230000004	0	1	1
102	15	13.77999973	4.699999809	41	2	12	13.15999985	4.070000172	1	1	1
178	4	9.649999619	9.649999619	64	3	12	9.020000458	9.010000229	1	1	1
115	2	2.190000057	2.190000057	41	9	16	2.150000095	2.150000095	1	2	1
128	13	0.5	0.5	62	8	16	0.289999992	0.289999992	0	2	1
99	35	12.76000023	2.730000019	62	2	12	12.10000038	2.069999933	1	1	1
133	-2	4.489999771	0.509999991	71	11	16	4.230000019	0.25	0	3	1
158	12	5.139999866	2.039999962	55	10	12	4.130000114	1.029999971	1	3	1
125	0	6.940000057	6.940000057	62	8	16	6	6	1	2	1
113	2	1.879999995	0.389999986	73	8	14	1.75	0.259999991	0	2	1
121	-12	6.349999905	0.280000001	73	17	18	6.289999962	0.219999999	0	4	1
172	10	3.779999971	3.779999971	72	8	16	3.029999971	3.029999971	1	2	1
159	49	11.69999981	11.69999981	64	8	14	11.67000008	11.67000008	1	2	1
135	14	6.099999905	3.170000076	55	4	13	5.829999924	2.900000095	1	1	1
155	7	7.590000153	5.289999962	55	10	18	7.320000172	5.019999981	1	3	1
128	22	0.560000002	0.560000002	41	2	13	0.310000002	0.310000002	0	1	1
127	62	3.420000076	3.420000076	73	10	16	3.170000076	3.170000076	1	3	1
134	45	0.310000002	0.310000002	62	8	16	0.370000005	0.370000005	0	2	1
126	13	0.769999981	0.439999998	55	2	12	0.289999992	0.050000001	0	1	1
131	16	4.239999771	4.239999771	41	10	18	4.050000191	4.050000191	1	3	1
136	-2	0.959999979	0.959999979	55	2	12	0.239999995	0.239999995	0	1	1
155	8	0.370000005	0.370000005	41	11	16	0.270000011	0.270000011	0	3	1
125	17	0.419999987	0.419999987	40	13	16	0.300000012	0.300000012	0	4	1
128	21	0.389999986	0.389999986	72	8	14	0.310000002	0.310000002	0	2	1
164	3	4.869999886	4.869999886	64	8	14	4.010000229	4.010000229	1	2	1
90	27	0.74000001	0.74000001	72	2	12	0.319999993	0.319999993	0	1	1
146	-5	4.28000021	2.789999962	73	11	14	3.470000029	1.99000001	1	3	1
159	19	0.920000017	0.280000001	55	14	20	0.949999988	0.300000012	0	4	1
125	12	4.800000191	4.800000191	74	8	16	4.039999962	4.039999962	1	2	1
129	36	3.420000076	3.420000076	62	8	14	3.099999905	3.099999905	1	2	1
149	4	2.609999895	1.279999971	63	8	16	2.339999914	1.00999999	1	2	1
182	-7	7.340000153	7.340000153	72	10	16	6.980000019	6.980000019	1	3	1
172	42	3.75999999	2.339999914	62	10	14	3.789999962	2.380000114	1	3	1
137	-11	6.519999981	0.280000001	71	17	16	6.46999979	0.219999999	0	4	1
171	30	3.160000086	2.75	62	3	12	2.5	2.079999924	1	1	1
144	34	1.269999981	0.730000019	55	3	12	1.090000033	0.550000012	1	1	1
163	28	1.389999986	1.389999986	61	8	14	1.090000033	1.080000043	1	2	1
165	4	6.889999866	5.119999886	74	8	16	6.75	4.980000019	1	2	1
128	11	6.519999981	5.389999866	72	3	12	6.170000076	5.03000021	1	1	1
133	6	1.289999962	1.289999962	63	8	14	1.019999981	1.019999981	1	2	1
162	-5	4.949999809	4.949999809	64	8	14	3.99000001	3.99000001	1	2	1
119	8	0.529999971	0.529999971	65	8	16	0.270000011	0.270000011	0	2	1
131	34	0.370000005	0.370000005	74	4	12	0.349999994	0.349999994	0	1	1
149	62	2.420000076	0.74000001	55	9	12	2.099999905	0.419999987	0	2	1
167	24	0.370000005	0.370000005	41	2	12	0.319999993	0.319999993	0	1	1
136	13	1.309999943	1.309999943	63	3	14	1.039999962	1.039999962	1	1	1
150	21	0.560000002	0.560000002	41	2	14	0.310000002	0.310000002	0	1	1
135	8	0.810000002	0.810000002	73	10	14	0.270000011	0.270000011	0	3	1
176	64	17.23999977	17.23999977	62	3	12	17.19000053	17.19000053	1	1	1
115	19	0.330000013	0.330000013	72	8	18	0.300000012	0.300000012	0	2	1
155	0	5.860000134	5.860000134	65	3	12	5	5	1	1	1
127	-12	1.169999957	1.169999957	62	3	13	0.970000029	0.970000029	1	1	1
61	37	4.71999979	0.280000001	62	6	14	4.789999962	0.349999994	0	1	1
115	15	3.160000086	0.860000014	55	2	13	2.579999924	0.280000001	0	1	1
121	23	1.690000057	0.709999979	55	2	14	1.289999962	0.310000002	0	1	1
160	-14	1.419999957	1.419999957	72	8	14	0.959999979	0.959999979	1	2	1
162	-1	12.57999992	3.99000001	72	13	14	11.59000015	3	1	4	1
155	4	2.859999895	2.859999895	72	8	14	2.00999999	2.00999999	1	2	1
124	-2	5.320000172	0.509999991	73	10	16	5.050000191	0.25	0	3	1
141	12	1.419999957	0.74000001	73	5	14	0.959999979	0.280000001	0	1	1
124	13	1.24000001	1.24000001	61	8	14	1.039999962	1.039999962	1	2	1
131	79	4.760000229	4.760000229	63	8	14	4.21999979	4.21999979	1	2	1
111	9	4.349999905	2.690000057	73	3	12	3.690000057	2.019999981	1	1	1
135	10	4.010000229	0.560000002	62	10	14	3.700000048	0.280000001	0	3	1
164	33	7.639999866	7.639999866	64	8	14	7.599999905	7.599999905	1	2	1
127	5	0.460000008	0.460000008	62	8	14	0.270000011	0.270000011	0	2	1
111	3	4.909999847	0.509999991	73	10	16	4.670000076	0.259999991	0	3	1
171	31	8.100000381	6.5	61	3	12	7.679999828	6.090000153	1	1	1
123	27	2.730000019	2.730000019	74	8	14	2.069999933	2.069999933	1	2	1
128	15	0.939999998	0.939999998	62	8	16	0.289999992	0.289999992	0	2	1
128	-6	0.629999995	0.629999995	62	8	16	0.239999995	0.239999995	0	2	1
132	-12	0.879999995	0.879999995	70	6	16	0.209999993	0.209999993	1	1	1
173	34	8.729999542	8.729999542	63	8	14	8.100000381	8.100000381	1	2	1
126	36	0.899999976	0.540000022	72	3	12	0.720000029	0.349999994	0	1	1
120	8	2.960000038	1.129999995	62	8	14	2.019999981	0.200000003	0	2	1
121	30	0.959999979	0.959999979	65	3	12	0.330000013	0.330000013	0	1	1
111	12	0.920000017	0.920000017	74	8	14	0.280000001	0.280000001	0	2	1
129	58	0.959999979	0.959999979	61	3	14	0.409999996	0.409999996	0	1	1
132	9	2.519999981	2.519999981	71	10	16	2.069999933	2.069999933	1	3	1
75	10	10.89999962	6.5	55	10	16	10.92000008	6.53000021	1	3	1
157	6	12.76000023	12.76000023	73	4	12	12.02000046	12.02000046	1	1	1
155	20	7.389999866	3.119999886	73	13	16	7.329999924	3.049999952	1	4	1
152	-2	3.279999971	3.279999971	62	8	14	2.99000001	2.99000001	1	2	1
121	5	5.809999943	0.920000017	62	3	12	5.150000095	0.259999991	0	1	1
112	18	0.939999998	0.939999998	62	8	14	1.299999952	1.299999952	1	2	1
170	4	3.420000076	3.420000076	62	8	16	3.00999999	3.00999999	1	2	1
159	13	4.800000191	4.800000191	65	8	16	4.039999962	4.039999962	1	2	1
124	17	0.649999976	0.649999976	72	8	14	0.300000012	0.300000012	0	2	1
174	-7	3.440000057	3.440000057	62	8	16	2.980000019	2.980000019	1	2	1
120	9	2.440000057	1.129999995	74	13	16	1.580000043	0.280000001	0	4	1
139	0	1.960000038	0.889999986	55	10	14	1.309999943	0.239999995	0	3	1
139	0	2.75999999	2.75999999	72	2	12	2	2	1	1	1
160	-3	1.690000057	1.350000024	41	14	18	1.330000043	0.99000001	1	4	1
133	-3	5.349999905	5.349999905	72	8	14	4.989999771	4.989999771	1	2	1
147	14	7.559999943	7.559999943	64	8	16	7.559999943	7.559999943	1	2	1
126	15	0.519999981	0.519999981	61	8	18	0.289999992	0.289999992	0	2	1
112	-3	6.78000021	0.280000001	64	13	18	6.739999771	0.239999995	0	4	1
140	16	0.959999979	0.74000001	72	3	13	0.519999981	0.289999992	0	1	1
124	60	1.879999995	0.389999986	62	10	14	1.909999967	0.419999987	0	3	1
104	10	1.99000001	1.99000001	72	2	14	1.029999971	1.029999971	1	1	1
126	30	2.779999971	0.270000011	73	8	14	2.839999914	0.330000013	0	2	1
140	20	5.050000191	0.910000026	41	4	12	4.429999828	0.300000012	0	1	1
106	7	8.149999619	0.75	71	9	12	7.670000076	0.270000011	0	2	1
138	7	0.730000019	0.730000019	72	4	12	0.270000011	0.270000011	0	1	1
135	5	2.230000019	0.810000002	55	3	12	1.679999948	0.270000011	0	1	1
105	35	0.280000001	0.280000001	72	8	16	0.349999994	0.349999994	0	2	1
143	2	14.27000046	14.27000046	73	11	16	14.02999973	14.02999973	1	3	1
131	27	2.940000057	2.690000057	55	10	18	1.320000052	1.070000052	1	3	1
108	-10	11.27999973	0.280000001	74	17	14	11.22000027	0.219999999	0	4	1
171	-7	5.329999924	2.079999924	72	10	14	4.380000114	1.129999995	1	3	1
152	22	2.670000076	2.230000019	55	5	13	2.5	2.059999943	1	1	1
171	15	5.889999866	5.21999979	64	3	12	5.71999979	5.039999962	1	1	1
152	8	1.960000038	1.960000038	62	2	12	1.019999981	1.019999981	1	1	1
115	69	0.460000008	0.319999993	72	3	12	0.579999983	0.439999998	0	1	1
80	8	0.479999989	0.479999989	41	4	12	0.270000011	0.270000011	0	1	1
115	15	2.130000114	0.360000014	41	5	16	2.059999943	0.289999992	0	1	1
134	-8	7.349999905	0.280000001	61	13	14	7.300000191	0.230000004	0	4	1
132	10	1.690000057	0.74000001	55	3	13	1.230000019	0.280000001	0	1	1
137	19	12.69999981	0.280000001	55	17	18	12.72000027	0.300000012	0	4	1
129	12	2.700000048	0.939999998	62	3	13	2.046999931	0.280000001	0	1	1
154	11	16.85000038	13.51000023	41	14	14	16.59000015	13.25	1	4	1
113	2	5.900000095	0.980000019	71	13	14	5.179999828	0.25	0	4	1
104	5	1.99000001	1.99000001	55	2	12	1.00999999	1.00999999	1	1	0
131	-4	1.100000024	1.100000024	72	8	14	0.239999995	0.239999995	0	2	0
117	34	0.810000002	0.810000002	62	8	14	0.349999994	0.349999994	0	2	0
171	-7	18.14999962	13.78999996	65	13	14	17.34000015	12.98999977	1	4	0
90	9	1.190000057	1.190000057	74	8	14	0.280000001	0.280000001	0	2	0
123	6	1.25	1.25	74	8	14	0.270000011	0.270000011	0	2	0
101	-3	8.25	4.489999771	62	13	16	7.760000229	3.99000001	1	4	0
40	87	0.959999979	0.959999979	62	8	18	0.479999989	0.479999989	0	2	0
117	6	2.799999952	2.799999952	74	8	14	2.019999981	2.019999981	1	2	0
132	9	1.269999981	1.269999981	74	8	14	1.019999981	1.019999981	1	2	0
159	-14	1.840000033	1.840000033	72	2	18	0.959999979	0.959999979	1	1	0
105	26	11.38000011	10.13000011	55	4	12	10.81999969	9.569999695	1	1	0
106	6	2.049999952	0.639999986	73	8	14	1.679999948	0.270000011	0	2	0
116	10	0.579999983	0.579999983	41	3	12	0.280000001	0.280000001	0	1	0
171	21	2.74000001	2.74000001	62	8	16	2.059999943	2.059999943	1	2	0
143	35	7.519999981	5.320000172	65	8	16	7.329999924	5.119999886	1	2	0
90	3	0.649999976	0.649999976	74	8	14	0.259999991	0.259999991	0	2	0
115	24	0.920000017	0.920000017	41	3	12	0.310000002	0.310000002	0	1	0
117	10	0.419999987	0.419999987	71	8	16	0.280000001	0.280000001	0	2	0