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researchv10 Norman

.EQ
delim $$
.EN
.LP
.ce
.ul
TABLE 12.1
.ce
SAMPLING DISTRIBUTIONS OF $y bar$, $y hat sub med$, $y hat sub w$
.ce
[3 from 8 Taxpayers]
.sp
.ls 1
.TS
c c c c c 
c c c c c 
n n n n n .
SAMPLE	SAMPLED	$y bar$	$y hat sub med$	$y hat sub w$
NUMBER	TAXPAYERS

1	1  2  3	66.67	68.00	67.33
55	5  7  8	112.00	116.00	114.00
56	6  7  8	116.00	116.00	116.00

TOTAL		5124.00	5052.00	5088.00

EXPECTATION		91.50	90.21	90.87

VARIANCE	122.76	211.26	153.97
.TE
.ls 2
.PP
First notice that the expectation of $y hat sub med$ is
samples of size 3 from the complete population.
.ce
.ul
TABLE 12.2
.ce
SAMPLING DISTRIBUTION OF $y bar$, $y hat sub med$, $y hat sub w$, $y hat sub A$
.ce
[3 Taxpayers from 9]
.sp
.ls 1
.TS
c c c c c c 
c c c c c c 
n n n n n n .
SAMPLE	SAMPLED	$y bar$	$Y hat sub med$	$y hat sub w$	$y hat sub A$
NUMBER	TAXPAYERS

1	1  2  3	66.67	68.00	67.33	71.67
2	1  2  4	75.33	72.00	73.67	80.33
3	1  2  5	74.00	72.00	73.00	79.00
4	1  2  6	78.00	72.00	75.00	83.00
5	1  2  7	82.67	72.00	77.33	87.67
6	1  2  8	87.33	72.00	79.67	92.33
7	1  2  9	110.67	72.00	91.33	110.67
8	1  3  4	74.00	68.00	71.00	79.00
9	1  3  5	72.67	68.00	70.33	77.67
10	1  3  6	76.67	68.00	72.33	81.67
11	1  3  7	81.33	68.00	74.67	86.33
12	1  3  8	86.00	68.00	77.00	91.00
13	1  3  9	109.33	68.00	88.67	109.33
14	1  4  5	81.33	90.00	85.67	86.33
15	1  4  6	85.33	94.00	89.67	90.33
16	1  4  7	90.00	94.00	92.00	95.00
17	1  4  8	94.67	94.00	94.33	99.67
18	1  4  9	118.00	94.00	106.00	118.00
19	1  5  6	84.00	90.00	87.00	89.00
20	1  5  7	88.67	90.00	89.33	93.67
21	1  5  8	93.33	90.00	91.67	98.33
22	1  5  9	116.67	90.00	103.33	116.67
23	1  6  7	92.67	102.00	97.33	97.67
24	1  6  8	97.33	102.00	99.67	102.33
25	1  6  9	120.67	102.00	111.33	120.67
26	1  7  8	102.00	116.00	109.00	107.00
27	1  7  9	125.33	116.00	120.67	125.33
28	1  8  9	130.00	130.00	130.00	130.00
29	2  3  4	78.00	72.00	75.00	78.00
30	2  3  5	76.67	72.00	74.33	76.67
31	2  3  6	80.67	72.00	76.33	80.67
32	2  3  7	85.33	72.00	78.67	85.33
33	2  3  8	90.00	72.00	81.00	90.00
34	2  3  9	113.33	72.00	92.67	108.33
35	2  4  5	85.33	90.00	87.67	85.33
36	2  4  6	89.33	94.00	91.67	89.33
37	2  4  7	94.00	94.00	94.00	94.00
38	2  4  8	98.67	94.00	96.33	98.67
39	2  4  9	122.00	94.00	108.00	117.00
40	2  5  6	88.00	90.00	89.00	88.00
41	2  5  7	92.67	90.00	91.33	92.67
42	2  5  8	97.33	90.00	93.67	97.33
43	2  5  9	120.67	90.00	105.33	115.67
44	2  6  7	96.67	102.00	99.33	96.67
45	2  6  8	101.33	102.00	101.67	101.33
46	2  6  9	124.67	102.00	113.33	119.67
47	2  7  8	106.00	116.00	111.00	106.00
48	2  7  9	129.33	116.00	122.67	124.33
49	2  8  9	134.00	130.00	132.00	129.00
50	3  4  5	84.00	90.00	87.00	84.00
51	3  4  6	88.00	94.00	91.00	88.00
52	3  4  7	92.67	94.00	93.33	92.67
53	3  4  8	97.33	94.00	95.67	97.33
54	3  4  9	120.67	94.00	107.33	115.67
55	3  5  6	86.67	90.00	88.33	86.67
56	3  5  7	91.33	90.00	90.67	91.33
57	3  5  8	96.00	90.00	93.00	96.00
58	3  5  9	119.33	90.00	104.67	114.33
59	3  6  7	95.33	102.00	98.66	95.33
60	3  6  8	100.00	102.00	101.00	100.00
61	3  6  9	123.33	102.00	112.67	118.33
62	3  7  8	104.67	116.00	110.33	104.67
63	3  7  9	128.00	116.00	122.00	123.00
64	3  8  9	132.67	130.00	131.33	127.67
65	4  5  6	95.33	94.00	94.67	95.33
66	4  5  7	100.00	94.00	97.00	100.00
67	4  5  8	104.67	94.00	99.33	104.67
68	4  5  9	128.00	94.00	111.00	123.00
69	4  6  7	104.00	102.00	103.00	104.00
70	4  6  8	108.67	102.00	105.33	108.67
71	4  6  9	132.00	102.00	117.00	127.00
72	4  7  8	113.33	116.00	114.67	113.33
73	4  7  9	136.67	116.00	126.33	131.67
74	4  8  9	141.33	130.00	135.67	136.33
75	5  6  7	102.67	102.00	102.33	102.67
76	5  6  8	107.33	102.00	104.67	107.33
77	5  6  9	130.67	102.00	116.33	125.67
78	5  7  8	112.00	116.00	114.00	112.00
79	5  7  9	135.33	116.00	125.67	130.33
80	5  8  9	140.00	130.00	135.00	135.00
81	6  7  8	116.00	116.00	116.00	116.00
82	6  7  9	139.33	116.00	127.67	134.33
83	6  8  9	144.00	130.00	137.00	139.00
84	7  8  9	148.67	130.00	139.33	143.67

TOTAL		8698.67	8026.00	8362.33	8698.67

MEAN		103.56	95.55	99.55	103.56

VARIANCE		405.32	314.51	318.63	301.12
.TE
.ls 2
.PP
In summary, the variance results are,

This archive runs on limited infrastructure. Preserving old code on modern bandwidth. Automated agents are requested to crawl responsibly.