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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

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 photos attached are the data collected for each of the 150 managers.

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? conclusion at the ?? = 5% level?

c) Obtain the 95% confidence interval for the proportion of the recruited from outside the Obtain the p-value corresponding to your hypotheses formulated in a) and give your company and briefly give the interpretation of this interval.

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Id Performance Salary Years Ext-Int Origin Perf-Ext Perf-Int 8.5 93 7 1 External 8.5 4.1 4.1 59 10 0 Internal 5.8 8.3 5.8 75 6 1 External 4.8 7.0 4.8 69 8 1 External 7.3 2.6 8.3 77 17 0 Internal 7.7 8.6 7.0 76 5 0 Internal 9.1 7.8 7.3 88 4 1 External 7.1 6.0 7.7 83 9 1 External 4.9 4.8 9.1 100 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 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 5.8 63 15 0 Internal 5.7 8.9 4.6 69 10 0 Internal 6.5 5.4 4.6 62 4 0 Internal 6.3 3.1 20 5.7 75 5 1 External 8.2 6.6 5.9 74 6 0 Internal 5.3 6.9 6.8 74 7 0 Internal 5.0 7.8 7.7 91 3 1 External 9.1 5.3 7.6 63 13 0 Internal 4.4 6.2 3.7 58 8 0 Internal 6.3 8.1 8.0 79 15 0 Internal 5.4 5.4 7.4 64 5 1 External 3.8 1.8 5.2 73 6 1 External 4.8 5.0 7.0 77 6 1 External 5.4 3.6 8.9 70 10 0 Internal 5.9 6.3 5.4 66 14 0 Internal 4.5 5.1 3.1 51 6 0 Internal 4.7 6.1 5.8 76 5 1 External 6.7 3.4 8.8 89 10 1 External 5.0 6.0 6.6 85 5 0 Internal 4.2 6.6 6.9 61 12 0 Internal 6.7 4.7 7.8 87 10 0 Internal 6.2 4.8 5.3 68 7 0 Internal 7.2 5.7 6.2 73 9 0 Internal 6.7 4.6 40 B. 1 80 16 0 Internal 7.5 6.6 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 1.8 55 6 0 Internal 5.7 4.1 6.5 88 3 1 External 5.2 5.0 6.3 64 8 1 External 4.8 6.1 5.0 59 8 0 Internal 7.3 3.9 3.6 69 3 0 Internal 7.0 5.5 8.2 82 11 1 External 9.0 7.6 6.3 84 4 0 Internal 6.1 2.7 5.1 76 11 0 Internal 7.1 7.4 6.1 82 16 0 Internal 5.0 6.8 3.4 59 7 0 Internal 5.2 5.3 6.0 61 11 0 Internal 6.0 3.9 6.6 64 16 0 Internal 8.1 5.0 4.7 59 7 0 Internal 7.1 6.5 5.3 68 7 1 External 5.4 5.2 5.0 68 6 1 External 7.3 6.1 4.8 67 16 0 Internal 5.6 4.6 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 4.765 5.6 67 0 Internal 7.6 66 4.0 62 0 Internal 7.9 67 6.3 85 1 External 4.2 68 5.4 84 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 0 Internal 4.7 75 4.8 74 1 External 4.3 76 5.4 61 1 External 3.9 77 5.5 70 0 Internal 5.5 78 7.6 82 0 Internal 6.1 79 5.9 70 1 External 6.0 80 4.5 62 1 External 4.6 81 4.7 71 1 External 3.9 82 6.7 89 1 External 5.5 83 5.0 74 1 External 4.6 84 4.2 67 1 External 6.2 85 2.7 72 0 Internal 7.5 86 7.4 99 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 IN 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 1 External 113 4.2 65 8 0 Internal 114 7.3 76 1 External 115 7.0 81 1 External 116 7.0 73 0 Internal 117 9.0 85 7 1 External 118 9.0 90 0 Internal 119 6.1 72 1 External 120 5.8 68 0 Internal 121 7.1 81 1 External 122 5.0 67 1 External 123 5.2 84 1 External 124 4.5 63 0 Internal 125 6.0 78 1 External 126 5.8 66 0 Internal 127 3.7 61 0 Internal 128 8.1 98 1 External 129 4.7 61 5 0 Internal 130 4.3 61 13 0 Internal131 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 1 External

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