Can you please answer the following question step by step, with full details for each answer.

Take your time but please make sure that the answers are fully detailed and correct.

The XYX recruiting firm offers its services to recruit the best managers either from inside or outside the company. In the business world, some people claim that the managers hired from outside of the company obtain better Performances than the ones recruited from within the company.

A team of researchers asked 150 managers, chosen at random, to take part in a small study in order to verify this business world's claim. The sample was obtained using a simple random draw. The file part2.xlsx contains the data collected for each of the 150 managers.

1) Find the minimum, the maximum, the mean and the standard deviation of the 150 managers salaries for the sample data.

a) Obtain a 95% confidence interval for the true mean salaries and briefly interpret the confidence interval.

b) From the confidence interval for the true mean salaries found in a), define if the p-value to confront the hypotheses H0: = 70 against HA: 70, would be higher, lower or equal to 5%. Briefly justify your answer.

2)

a) Perform a simple linear regression using Salary as the independent variable and a multiple regression using Salary, Years of experience and Origin as independent variables.

b) Which one of the multiple and simple linear regression models seems to be the best to predict the dependent variable Performance and why?

c) Is Origin a significant variable? Why.

d) Show your final model, and briefly interpret the coefficients of this model as well as the coefficient of determination.

3) Although many people from the business world claim that the managers recruited from outside the company obtain better performances, we want to verify the proportion of managers recruited from outside the company is lower than 50%.

a) Precisely formulate the hypotheses H0 and HA that we want to confront in this problem.

b) In the sample, what is the proportion of managers recruited from outside the company? Obtain the p-value corresponding to your hypotheses formulated in a) and give your conclusion at the = 5% level?

c) Obtain the 95% confidence interval for the proportion of the recruited from outside the company and briefly give the interpretation of this interval.

Id	Performance	Salary	Years	Ext-Int	Origin	Perf-Ext	Perf-Int
1	8.5	93	7	1	External	8.5	4.1
2	4.1	59	10	0	Internal	5.8	8.3
3	5.8	75	6	1	External	4.8	7.0
4	4.8	69	8	1	External	7.3	2.6
5	8.3	77	17	0	Internal	7.7	8.6
6	7.0	76	5	0	Internal	9.1	7.8
7	7.3	88	4	1	External	7.1	6.0
8	7.7	83	9	1	External	4.9	4.8
9	9.1	100	7	1	External	5.7	5.8
10	7.1	86	4	1	External	7.7	4.6
11	2.6	53	14	0	Internal	7.4	4.6
12	8.6	78	9	0	Internal	5.2	5.9
13	7.8	69	19	0	Internal	7.0	6.8
14	6.0	87	11	0	Internal	5.8	7.6
15	4.8	67	5	0	Internal	8.8	3.7
16	4.9	76	0	1	External	7.6	8.0
17	5.8	63	15	0	Internal	5.7	8.9
18	4.6	69	10	0	Internal	6.5	5.4
19	4.6	62	4	0	Internal	6.3	3.1
20	5.7	75	5	1	External	8.2	6.6
21	5.9	74	6	0	Internal	5.3	6.9
22	6.8	74	7	0	Internal	5.0	7.8
23	7.7	91	3	1	External	9.1	5.3
24	7.6	63	13	0	Internal	4.4	6.2
25	3.7	58	8	0	Internal	6.3	8.1
26	8.0	79	15	0	Internal	5.4	5.4
27	7.4	64	5	1	External	3.8	1.8
28	5.2	73	6	1	External	4.8	5.0
29	7.0	77	6	1	External	5.4	3.6
30	8.9	70	10	0	Internal	5.9	6.3
31	5.4	66	14	0	Internal	4.5	5.1
32	3.1	51	6	0	Internal	4.7	6.1
33	5.8	76	5	1	External	6.7	3.4
34	8.8	89	10	1	External	5.0	6.0
35	6.6	85	5	0	Internal	4.2	6.6
36	6.9	61	12	0	Internal	6.7	4.7
37	7.8	87	10	0	Internal	6.2	4.8
38	5.3	68	7	0	Internal	7.2	5.7
39	6.2	73	9	0	Internal	6.7	4.6
40	8.1	80	16	0	Internal	7.5	6.6
41	7.6	81	5	1	External	8.5	5.6
42	5.4	65	11	0	Internal	4.9	4.0
43	5.7	74	5	1	External	5.7	6.2
44	1.8	55	6	0	Internal	5.7	4.1
45	6.5	88	3	1	External	5.2	5.0
46	6.3	64	8	1	External	4.8	6.1
47	5.0	59	8	0	Internal	7.3	3.9
48	3.6	69	3	0	Internal	7.0	5.5
49	8.2	82	11	1	External	9.0	7.6
50	6.3	84	4	0	Internal	6.1	2.7
51	5.1	76	11	0	Internal	7.1	7.4
52	6.1	82	16	0	Internal	5.0	6.8
53	3.4	59	7	0	Internal	5.2	5.3
54	6.0	61	11	0	Internal	6.0	3.9
55	6.6	64	16	0	Internal	8.1	5.0
56	4.7	59	7	0	Internal	7.1	6.5
57	5.3	68	7	1	External	5.4	5.2
58	5.0	68	6	1	External	7.3	6.1
59	4.8	67	16	0	Internal	5.6	4.6
60	9.1	91	7	1	External	6.0	3.1
61	5.7	68	16	0	Internal	7.7	5.2
62	4.6	53	10	0	Internal	5.3	4.5
63	4.4	68	7	1	External		6.0
64	6.6	81	5	0	Internal		4.7
65	5.6	67	14	0	Internal		7.6
66	4.0	62	7	0	Internal		7.9
67	6.3	85	6	1	External		4.2
68	5.4	84	5	1	External		7.0
69	6.2	57	6	0	Internal		9.0
70	4.1	61	15	0	Internal		5.8
71	3.8	62	4	1	External		4.5
72	5.0	59	11	0	Internal		5.8
73	6.1	67	12	0	Internal		3.7
74	3.9	53	9	0	Internal		4.7
75	4.8	74	5	1	External		4.3
76	5.4	61	5	1	External		3.9
77	5.5	70	10	0	Internal		5.5
78	7.6	82	4	0	Internal		6.1
79	5.9	70	8	1	External		6.0
80	4.5	62	4	1	External		4.6
81	4.7	71	3	1	External		3.9
82	6.7	89	6	1	External		5.5
83	5.0	74	8	1	External		4.6
84	4.2	67	7	1	External		6.2
85	2.7	72	7	0	Internal		7.5
86	7.4	66	12	0	Internal		6.3
87	6.8	65	11	0	Internal		7.2
88	5.3	57	21	0	Internal		6.2
89	6.7	81	5	1	External
90	6.2	75	6	1	External
91	7.2	80	8	1	External
92	3.9	70	8	0	Internal
93	6.7	81	7	1	External
94	7.5	76	8	1	External
95	5.0	67	16	0	Internal
96	6.5	74	10	0	Internal
97	8.5	103	2	1	External
98	5.2	68	11	0	Internal
99	4.9	76	3	1	External
100	6.1	64	10	0	Internal
101	4.6	57	5	0	Internal
102	3.1	48	10	0	Internal
103	5.2	66	5	0	Internal
104	4.5	63	13	0	Internal
105	5.7	76	5	1	External
106	5.7	74	7	1	External
107	6.0	59	15	0	Internal
108	4.7	60	9	0	Internal
109	7.6	73	15	0	Internal
110	5.2	77	4	1	External
111	7.9	63	17	0	Internal
112	4.8	71	7	1	External
113	4.2	65	8	0	Internal
114	7.3	76	4	1	External
115	7.0	81	6	1	External
116	7.0	73	11	0	Internal
117	9.0	85	7	1	External
118	9.0	90	9	0	Internal
119	6.1	72	5	1	External
120	5.8	68	9	0	Internal
121	7.1	81	5	1	External
122	5.0	67	8	1	External
123	5.2	84	5	1	External
124	4.5	63	7	0	Internal
125	6.0	78	6	1	External
126	5.8	66	7	0	Internal
127	3.7	61	7	0	Internal
128	8.1	98	4	1	External
129	4.7	61	5	0	Internal
130	4.3	61	13	0	Internal
131	3.9	55	9	0	Internal
132	7.1	75	5	1	External
133	5.5	62	10	0	Internal
134	6.1	69	6	0	Internal
135	6.0	59	5	0	Internal
136	4.6	55	12	0	Internal
137	3.9	58	4	0	Internal
138	5.5	73	5	0	Internal
139	5.4	85	3	1	External
140	7.3	91	2	1	External
141	5.6	79	6	1	External
142	4.6	61	9	0	Internal
143	6.2	74	5	0	Internal
144	7.5	71	12	0	Internal
145	6.3	73	14	0	Internal
146	7.2	69	7	0	Internal
147	6.2	79	11	0	Internal
148	6.0	76	6	1	External
149	7.7	89	3	1	External
150	5.3	73	7	1	External