Confidence interval for the difference between means

Question

Discuss the below:

Q: Consider the file data on Taxes that is included in worksheet P2 on the exam template. This data represents property taxes paid by 170 residents that live in a small town. Assume this file to be the entire population. Answer the following questions:

a. A local politician in this town has stated that the average property taxes are $1800 and most people do not pay more than this amount. Conduct a test at the ? = .01 level to determine if this is true. For this test, consider a sample size of 30 households. Also, you want to have strong evidence to disclaim his hypothesis.

b. Find the probability of a Type two error when U = 2200

c. Conduct the same test as in part a, however, use sampling data by taking the fist 50 data points in the population

d. Conduct a test at the alpha = .05 level to determine if there is a difference between taxes paid in neighborhood 1 and in neighborhood 4. Use all the data points from both neighborhoods and consider this to be sample data.

e. From part d, what is the 95% confidence interval for the difference between means

Annual Real Estate Taxes Paid by Homeowners in a small town (Population Data)
Homeowner	Neighborhood	Tax_Paid
1	3	$1,138.92
2	2	$2,268.88
3	3	$1,712.93
4	3	$1,716.31
5	3	$1,599.98
6	4	$1,941.38
7	6	$980.24
8	5	$2,268.14
9	6	$1,868.73
10	1	$1,618.15
11	4	$1,705.31
12	1	$1,908.44
13	3	$1,145.30
14	2	$2,419.79
15	6	$1,632.89
16	6	$1,883.85
17	4	$1,800.83
18	6	$1,985.80
19	4	$1,929.04
20	4	$1,616.92
21	2	$1,925.38
22	2	$2,652.80
23	1	$2,319.15
24	6	$1,393.23
25	1	$2,616.94
26	3	$1,681.42
27	6	$952.51
28	1	$1,636.48
29	2	$2,648.90
30	1	$2,441.58
31	3	$2,078.22
32	6	$1,298.17
33	2	$2,868.10
34	4	$2,084.50
35	6	$1,653.76
36	5	$3,288.01
37	1	$1,848.47
38	3	$1,662.51
39	3	$1,449.33
40	3	$1,447.77
41	2	$2,414.60
42	3	$1,309.24
43	3	$1,519.18
44	1	$2,047.69
45	3	$1,686.12
46	4	$1,755.92
47	6	$1,781.70
48	6	$1,353.92
49	1	$1,818.35
50	1	$1,904.13
51	2	$2,816.79
52	3	$1,838.13
53	2	$2,866.46
54	1	$2,117.40
55	4	$1,960.53
56	5	$2,322.78
57	6	$1,366.77
58	4	$1,653.42
59	4	$1,667.42
60	3	$1,567.33
61	4	$1,544.65
62	5	$2,922.20
63	6	$1,574.00
64	3	$1,541.02
65	4	$1,528.53
66	6	$1,177.54
67	6	$1,723.23
68	6	$1,705.59
69	6	$1,468.23
70	6	$1,081.04
71	1	$2,136.10
72	6	$1,671.80
73	6	$867.18
74	1	$2,296.04
75	6	$1,398.27
76	3	$985.60
77	5	$3,168.90
78	6	$1,067.69
79	6	$1,230.40
80	5	$3,775.00
81	6	$2,025.42
82	6	$1,279.13
83	3	$1,459.57
84	6	$1,456.21
85	1	$1,900.65
86	6	$1,367.51
87	6	$1,554.98
88	3	$1,536.49
89	2	$2,428.34
90	6	$1,825.01
91	1	$1,596.91
92	4	$1,951.69
93	4	$1,694.57
94	4	$1,970.08
95	1	$2,265.39
96	3	$863.23
97	6	$1,229.90
98	3	$1,515.65
99	2	$2,332.28
100	5	$3,045.21
101	6	$1,190.32
102	3	$1,410.75
103	3	$1,813.82
104	2	$2,243.49
105	6	$1,280.51
106	6	$1,458.34
107	5	$3,121.92
108	2	$2,297.38
109	3	$1,538.36
110	6	$1,566.28
111	6	$1,609.09
112	3	$1,513.09
113	4	$1,673.89
114	4	$1,749.77
115	3	$1,553.90
116	5	$3,175.09
117	2	$2,514.27
118	3	$1,251.61
119	6	$1,690.06
120	3	$1,181.98
121	3	$1,175.79
122	6	$1,632.60
123	3	$1,563.36
124	3	$2,006.47
125	5	$3,000.34
126	3	$1,775.11
127	3	$1,510.54
128	5	$3,189.34
129	2	$2,396.58
130	3	$1,495.29
131	2	$2,350.90
132	4	$1,763.61
133	6	$1,094.63
134	2	$2,279.87
135	3	$1,705.94
136	4	$1,773.60
137	4	$1,830.08
138	5	$2,556.52
139	4	$1,758.91
140	3	$1,687.77
141	5	$3,056.78
142	3	$1,423.09
143	6	$2,006.56
144	3	$1,129.66
145	4	$1,808.78
146	5	$3,177.85
147	2	$2,628.84
148	6	$1,592.98
149	2	$2,309.48
150	6	$1,341.05
151	6	$1,313.94
152	6	$1,382.76
153	6	$1,786.41
154	6	$1,533.79
155	5	$2,963.82
156	1	$1,562.61
157	2	$2,420.67
158	6	$1,752.22
159	2	$2,437.49
160	6	$1,670.68
161	1	$1,730.73
162	1	$2,205.32
163	6	$937.85
164	3	$1,348.12
165	4	$1,762.19
166	3	$1,944.03
167	4	$1,759.98
168	6	$1,014.34
169	2	$2,670.30
170	6	$969.61