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1.1 root 1: .EQ
2: delim $$
3: .EN
4: .LP
5: .ce
6: .ul
7: TABLE 12.1
8: .ce
9: SAMPLING DISTRIBUTIONS OF $y bar$, $y hat sub med$, $y hat sub w$
10: .ce
11: [3 from 8 Taxpayers]
12: .sp
13: .ls 1
14: .TS
15: c c c c c
16: c c c c c
17: n n n n n .
18: SAMPLE SAMPLED $y bar$ $y hat sub med$ $y hat sub w$
19: NUMBER TAXPAYERS
20:
21: 1 1 2 3 66.67 68.00 67.33
22: 55 5 7 8 112.00 116.00 114.00
23: 56 6 7 8 116.00 116.00 116.00
24:
25: TOTAL 5124.00 5052.00 5088.00
26:
27: EXPECTATION 91.50 90.21 90.87
28:
29: VARIANCE 122.76 211.26 153.97
30: .TE
31: .ls 2
32: .PP
33: First notice that the expectation of $y hat sub med$ is
34: samples of size 3 from the complete population.
35: .ce
36: .ul
37: TABLE 12.2
38: .ce
39: SAMPLING DISTRIBUTION OF $y bar$, $y hat sub med$, $y hat sub w$, $y hat sub A$
40: .ce
41: [3 Taxpayers from 9]
42: .sp
43: .ls 1
44: .TS
45: c c c c c c
46: c c c c c c
47: n n n n n n .
48: SAMPLE SAMPLED $y bar$ $Y hat sub med$ $y hat sub w$ $y hat sub A$
49: NUMBER TAXPAYERS
50:
51: 1 1 2 3 66.67 68.00 67.33 71.67
52: 2 1 2 4 75.33 72.00 73.67 80.33
53: 3 1 2 5 74.00 72.00 73.00 79.00
54: 4 1 2 6 78.00 72.00 75.00 83.00
55: 5 1 2 7 82.67 72.00 77.33 87.67
56: 6 1 2 8 87.33 72.00 79.67 92.33
57: 7 1 2 9 110.67 72.00 91.33 110.67
58: 8 1 3 4 74.00 68.00 71.00 79.00
59: 9 1 3 5 72.67 68.00 70.33 77.67
60: 10 1 3 6 76.67 68.00 72.33 81.67
61: 11 1 3 7 81.33 68.00 74.67 86.33
62: 12 1 3 8 86.00 68.00 77.00 91.00
63: 13 1 3 9 109.33 68.00 88.67 109.33
64: 14 1 4 5 81.33 90.00 85.67 86.33
65: 15 1 4 6 85.33 94.00 89.67 90.33
66: 16 1 4 7 90.00 94.00 92.00 95.00
67: 17 1 4 8 94.67 94.00 94.33 99.67
68: 18 1 4 9 118.00 94.00 106.00 118.00
69: 19 1 5 6 84.00 90.00 87.00 89.00
70: 20 1 5 7 88.67 90.00 89.33 93.67
71: 21 1 5 8 93.33 90.00 91.67 98.33
72: 22 1 5 9 116.67 90.00 103.33 116.67
73: 23 1 6 7 92.67 102.00 97.33 97.67
74: 24 1 6 8 97.33 102.00 99.67 102.33
75: 25 1 6 9 120.67 102.00 111.33 120.67
76: 26 1 7 8 102.00 116.00 109.00 107.00
77: 27 1 7 9 125.33 116.00 120.67 125.33
78: 28 1 8 9 130.00 130.00 130.00 130.00
79: 29 2 3 4 78.00 72.00 75.00 78.00
80: 30 2 3 5 76.67 72.00 74.33 76.67
81: 31 2 3 6 80.67 72.00 76.33 80.67
82: 32 2 3 7 85.33 72.00 78.67 85.33
83: 33 2 3 8 90.00 72.00 81.00 90.00
84: 34 2 3 9 113.33 72.00 92.67 108.33
85: 35 2 4 5 85.33 90.00 87.67 85.33
86: 36 2 4 6 89.33 94.00 91.67 89.33
87: 37 2 4 7 94.00 94.00 94.00 94.00
88: 38 2 4 8 98.67 94.00 96.33 98.67
89: 39 2 4 9 122.00 94.00 108.00 117.00
90: 40 2 5 6 88.00 90.00 89.00 88.00
91: 41 2 5 7 92.67 90.00 91.33 92.67
92: 42 2 5 8 97.33 90.00 93.67 97.33
93: 43 2 5 9 120.67 90.00 105.33 115.67
94: 44 2 6 7 96.67 102.00 99.33 96.67
95: 45 2 6 8 101.33 102.00 101.67 101.33
96: 46 2 6 9 124.67 102.00 113.33 119.67
97: 47 2 7 8 106.00 116.00 111.00 106.00
98: 48 2 7 9 129.33 116.00 122.67 124.33
99: 49 2 8 9 134.00 130.00 132.00 129.00
100: 50 3 4 5 84.00 90.00 87.00 84.00
101: 51 3 4 6 88.00 94.00 91.00 88.00
102: 52 3 4 7 92.67 94.00 93.33 92.67
103: 53 3 4 8 97.33 94.00 95.67 97.33
104: 54 3 4 9 120.67 94.00 107.33 115.67
105: 55 3 5 6 86.67 90.00 88.33 86.67
106: 56 3 5 7 91.33 90.00 90.67 91.33
107: 57 3 5 8 96.00 90.00 93.00 96.00
108: 58 3 5 9 119.33 90.00 104.67 114.33
109: 59 3 6 7 95.33 102.00 98.66 95.33
110: 60 3 6 8 100.00 102.00 101.00 100.00
111: 61 3 6 9 123.33 102.00 112.67 118.33
112: 62 3 7 8 104.67 116.00 110.33 104.67
113: 63 3 7 9 128.00 116.00 122.00 123.00
114: 64 3 8 9 132.67 130.00 131.33 127.67
115: 65 4 5 6 95.33 94.00 94.67 95.33
116: 66 4 5 7 100.00 94.00 97.00 100.00
117: 67 4 5 8 104.67 94.00 99.33 104.67
118: 68 4 5 9 128.00 94.00 111.00 123.00
119: 69 4 6 7 104.00 102.00 103.00 104.00
120: 70 4 6 8 108.67 102.00 105.33 108.67
121: 71 4 6 9 132.00 102.00 117.00 127.00
122: 72 4 7 8 113.33 116.00 114.67 113.33
123: 73 4 7 9 136.67 116.00 126.33 131.67
124: 74 4 8 9 141.33 130.00 135.67 136.33
125: 75 5 6 7 102.67 102.00 102.33 102.67
126: 76 5 6 8 107.33 102.00 104.67 107.33
127: 77 5 6 9 130.67 102.00 116.33 125.67
128: 78 5 7 8 112.00 116.00 114.00 112.00
129: 79 5 7 9 135.33 116.00 125.67 130.33
130: 80 5 8 9 140.00 130.00 135.00 135.00
131: 81 6 7 8 116.00 116.00 116.00 116.00
132: 82 6 7 9 139.33 116.00 127.67 134.33
133: 83 6 8 9 144.00 130.00 137.00 139.00
134: 84 7 8 9 148.67 130.00 139.33 143.67
135:
136: TOTAL 8698.67 8026.00 8362.33 8698.67
137:
138: MEAN 103.56 95.55 99.55 103.56
139:
140: VARIANCE 405.32 314.51 318.63 301.12
141: .TE
142: .ls 2
143: .PP
144: In summary, the variance results are,
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