a. Conduct a t-test to compare the means of numbers for Roce, Prod, and Commit firms that have and do not have a scheme. c. Give a rationale for your findings.

It's worth noting that if the company has a profit-sharing plan, 1 means it does, and 0 means it doesn't.

Roce	Prod	Commit	Scheme
16.8	3.62	2.05	1
22.4	7.42	2.56	1
-3.5	1.56	1.71	1
16.8	4.34	1.79	1
16.1	4.62	1.93	1
26.6	6.7	2.06	1
9.8	2.94	2.19	1
21.7	7.58	2.08	1
23.1	7.5	2	1
18.2	7.86	2.09	1
28.7	8.45	2.64	1
18.9	6.87	2.22	1
17.5	5.42	2.41	1
16.1	4.25	1.92	1
15.4	5.19	2.03	1
26.6	8.72	2.05	1
-4.2	1.37	1.71	1
25.9	8.7	2.33	1
11.9	4.21	2.04	1
6.3	2.13	2.06	0
11.2	4.49	2.41	1
9.1	2.8	1.71	1
6.3	2.59	2.15	1
6.3	2.74	2.02	0
17.5	5.4	1.95	1
23.8	6.26	2.12	1
8.4	2.3	1.84	0
26.6	10.1	2.49	1
11.9	3.45	2.29	0
14.7	4.83	2.21	0
10.5	4.14	2.09	1
12.6	4.34	2.22	0
11.9	3.29	1.76	1
16.8	3.52	1.84	0
14.7	4.92	2.32	1
23.1	8.71	2.48	1
6.3	1.98	2.14	1
14	3.98	2.04	1
24.5	7.86	2.15	1
20.3	10.76	2.28	1
21	6.24	2.05	1
2.1	2.36	1.73	0
22.4	9.19	2.2	1
21.7	10.85	2.32	1
9.1	2.19	2	1
12.6	3.31	1.96	0
24.5	8.89	2.45	1
18.2	8.89	2.63	1
25.2	7.08	2.45	1
9.8	2.95	2.15	0
11.2	3.82	1.79	0
22.4	7.95	2.45	1
14	3.99	2.32	1
19.6	5.93	2.17	1
25.2	7.43	2.11	1
21	6.73	2.34	0
15.4	5.22	2.14	1
18.2	10.22	2.42	1
30.1	8.76	2.33	0
22.4	8.2	2.41	1
15.4	5.07	2.09	0
18.2	10.58	2.3	1
17.5	5.34	2.15	1
11.9	4.58	1.71	1
18.2	8.79	2.49	1
-4.2	1.48	2.01	0
21.7	6.36	2.03	1
19.6	5.66	2.12	1
18.2	7.92	2.41	1
23.8	9.5	2.68	1
6.3	2.7	1.65	1
15.4	5.05	2.09	1
24.5	10.37	2.09	1
11.9	3.21	2	1
20.3	10.58	2.32	1
16.1	5.31	2.04	1
13.3	3.55	1.93	1
23.8	8.5	2.08	1
11.2	4.58	2.4	0
37.8	14.4	2.81	1
18.2	5.46	2	0
18.2	5.54	1.89	1
10.5	4.76	2.22	1
-1.4	1.51	1.98	0
24.5	6.2	2.4	0
11.9	3.63	2.23	0
11.9	3.72	2.4	1
30.8	12.19	2.44	1
28	10.86	2.7	1
11.2	4.5	1.95	0
24.5	7.74	1.87	1
9.8	2.94	1.85	0
25.9	9.06	2.07	1
23.1	9.23	2.19	1
13.3	3.66	2.33	1
7	1.85	1.58	0
16.1	3.29	2.19	0
-2.8	1.56	1.67	0
12.6	4.11	1.68	1
9.8	2.91	2.03	1
13.3	3.86	2.08	0
2.8	2.04	1.78	1
22.4	6.55	2.56	0
24.5	6.4	2.34	1
0.7	1.55	2.01	0
8.4	2.07	1.98	0
16.1	3.8	2.18	0
19.6	6.04	2	1
12.6	4.16	2.16	1
18.2	8.7	2.22	1
14.7	4.86	1.71	1
20.3	6.15	2.22	0
12.6	4.22	2.26	1
21	6.65	2.37	1
0.7	1.02	1.63	0
3.5	2.01	1.64	0
11.2	3.39	1.89	0
16.1	5.34	2.36	1
11.2	4.21	2.23	1
14.7	4.31	2.22	1
24.5	7.74	2.43	0
2.8	1.98	2.07	1
10.5	3.1	2.03	1
2.1	2.36	1.85	1
7	1.8	1.82	1
11.9	3.21	2.46	0
23.1	7.1	2.18	1
21	6.98	2.58	1
24.5	8.33	2.25	1
2.8	2.18	2.38	0
8.4	1.98	2.04	0
2.8	2.14	1.62	0
30.8	12.21	2.72	1
18.9	7.1	2.28	1
4.9	2.41	2	1
9.8	2.91	1.74	0
28	6.47	2.37	1
8.4	2.63	1.87	0
18.2	7.96	2.67	1
15.4	5.2	2.33	1
14.7	3.43	2.11	0
21	6.44	2.3	1
11.9	3.75	1.97	1
14	3.93	2.05	1
30.8	9.26	2.5	1
21.7	9.03	2.54	1
16.8	3.64	2.03	0
18.2	5.54	2	1
22.4	6.42	2.13	1
13.3	3.89	1.87	1
0	1.01	1.87	0
4.2	2.65	2.27	0
17.5	5.46	2.12	1
14.7	3.82	2.08	0
11.9	4.48	2.22	0
19.6	5.8	2.46	0
11.2	4.12	2.07	0
14	4.63	2.28	0
8.4	2.29	1.75	1
14.7	4.08	2.22	0
10.5	3.19	1.86	1
3.5	2.13	1.96	0
18.2	5.5	2.23	1
20.3	7.26	2.19	1
4.9	2.3	1.69	0
11.2	4.43	2.01	1
20.3	9.67	2.48	1
15.4	5.08	2.24	1
16.1	4.1	1.96	0
18.9	7.25	2.42	1
18.9	10.47	2.3	1
28.7	6.21	2.2	0
19.6	5.75	2.59	1
16.1	3.35	2.13	1
16.8	3.31	2.35	1
14.7	3.31	1.94	1
23.8	9.55	2.25	1
6.3	2.72	1.75	1
19.6	5.79	2.5	1
12.6	4.51	2.38	1
22.4	8.82	2.53	1
37.8	13.34	2.55	1
9.8	3.03	1.77	0
10.5	4.61	2.32	0
15.4	5.1	1.89	1
11.2	3.71	1.84	0
13.3	3.73	2.06	0
7.7	2.32	2.43	1
8.4	2.55	1.63	0
28	10.26	2.02	1
19.6	5.62	2.09	1
31.5	12.6	2.48	1
11.2	3.59	2.19	0
12.6	4.25	2.05	1
7	1.79	2.21	1
17.5	5.41	2.2	0
13.3	4.36	2.23	1
16.1	4.34	1.88	1
8.4	2.5	1.75	0
15.4	5.12	2.04	1
6.3	2.71	1.97	0
12.6	4.29	2.07	1
21	8.04	2.48	1
21	6.76	2.11	1
10.5	3.5	2.07	1
14	3.95	2.05	0
4.9	1.93	1.97	0
23.1	9.18	2.38	0
21.7	7.5	1.91	1
10.5	3.17	2.23	1
9.8	3.04	2.05	0
28	8.97	2.27	1
9.1	2.87	2.12	0
39.2	15.5	2.53	1
32.2	12.96	2.65	1
28	9.5	2.47	1
24.5	6.32	2.15	0
21.7	10.24	2.48	1
21	6.93	2.29	1
24.5	8.85	2.41	1
7.7	1.89	2.03	0
32.9	13	2.4	1
10.5	3.14	1.81	1
9.1	2.75	2.01	0
10.5	3.17	1.96	0
16.8	3.62	2.15	1
14	4.66	2.35	0
30.8	11.08	2.63	1
14.7	4.84	2.15	1
20.3	6.14	2.41	1
14.7	4.85	2.26	1
6.3	2.75	1.83	1
21.7	6.43	2.5	1
23.1	10.75	2.45	1
14.7	4.93	1.98	1
20.3	6.1	2.25	1
3.5	1.95	1.77	1
14.7	4.95	2	1
17.5	5.44	2.34	1
14	4.46	1.93	1
8.4	2.25	2.2	0
18.9	6.55	2.06	1
26.6	9.28	2.56	1
-0.7	1.79	1.94	0
15.4	5.2	2.02	1
24.5	8.77	2.4	1
11.9	3.65	2.28	1
18.9	7.2	2.36	1
30.1	6.25	2.23	1
11.9	3.22	2.45	0
17.5	4.81	2.16	1
19.6	5.67	2.26	1
12.6	3.33	1.84	0
9.8	2.87	2.14	1
21.7	6.89	2.25	1
12.6	3.39	2.01	1
24.5	6.53	2.22	1
15.4	4.98	2.39	1
16.1	3.98	2.05	1
4.9	2.33	2.23	0
13.3	4.43	1.98	1
7	1.87	1.71	1
25.2	8.95	2.39	1
16.1	3.62	2.15	0
18.2	5.47	1.94	1
0.7	1.17	2.13	0
19.6	6.03	1.94	1
21.7	6.69	1.95	1
18.2	5.57	2.09	1
20.3	7.62	1.89	0
23.8	6.69	2.45	0
15.4	5.25	2.01	1
20.3	8.49	2.04	1
20.3	6.06	2.6	0
11.2	3.37	1.94	0
16.1	4.53	1.95	1
18.9	8.07	2.57	1
14.7	3.84	2.13	1
32.9	13.2	2.36	1
18.2	9.94	2.67	1