Question

In: Statistics and Probability

Assume the car expert requested estimates of the mean number of days to sell for the Domestic cars

6 Assume the car expert requested estimates of the mean number of days to sell for the Domestic cars with a margin of error of seven days and the mean number of days of Foreign cars with a margin of error of eight days. Using 98% confidence, how large should the sample sizes be for each?

7 Suppose a Domestic car has a list price of $30,000 and a Foreign car has a list price of $30,000. What is your estimate of the final selling price (based on the percent difference for the sale and list price) and number of days required to sell each of these cars?

	Domestic Cars			Foreign Cars
Car	List Price in K	Sale Price in K	Days to Sell	List Price in K	Sale Price in K	Days to Sell
1	6.1	4.4	36	83.1	78.5	101
2	67.6	66.8	51	59.6	57.1	62
3	14	13.4	87	37	32.5	63
4	83.4	80.5	80	43.4	43.2	47
5	40	35.4	38	16.3	15	93
6	56	52	24	8.3	5.9	21
7	71.2	68.7	27	29.2	27.5	107
8	50.7	49.7	52	32.7	32.7	15
9	4.9	4.3	74	23.9	23.5	12
10	70.5	66.5	84	85.5	85.1	58
11	58	56	30	19	16.3	96
12	75	73.7	31	19	18.9	106
13	2.8	1.1	88	80.8	77.4	50
14	7.7	4	11	17.7	15.6	42
15	20	16.2	20	71.4	70.4	75
16	23	21.5	71	16.1	13.8	62
17	6.2	6	88	49.2	45.2	91
18	18	14	43	40	38	6
19	97	93.2	95	32	29.2	52
20	69.2	66.8	37	27.2	22.5	71
21	63.5	60.7	13	85.5	82.8	106
22	65	61.9	60	87.4	85.7	91
23	9.9	7	24	58.9	56.9	83
24	90.2	88.3	42	56.2	52.8	29
25	56	55	91	13.5	10	76
26	80	75.2	39	55.7	54.2	40
27	58.7	58.3	58	75.7	74.6	47
28	33.1	32.9	47	89.1	85.7	67
29	31.5	28.7	86	3.5	3.2	106
30	54.5	54.1	88	67.5	65.3	100
31	22.4	17.8	30	41.4	40.1	10
32	40.3	38.4	29	45.3	43.3	36
33	27.2	22.6	34	87.2	85.1	61
34	14.4	14.1	12	16.4	14.3	65
35	5.6	1.5	86	32.6	29.1	25
36	42.2	40.8	72	14.2	14.2	39
37	9.5	6.2	69	60.5	59.1	79
38	93.1	90.5	32	73.1	68.3	83
39	10.7	7.3	15	48.7	44.7	65
40	93.3	91.7	15	38.3	38.2	35
41	50	49.1	19	6.6	4.3	6
42	33.2	29.6	27	86.2	81.4	53
43	67	60	18	5	4.6	108
44	56	53.1	54	37	32.7	85
45	49.5	48.2	37	23.5	21.2	32
46	52.7	48.8	66	90.7	87.4	97
47	41.1	39.7	78	84.1	83.8	16
48	72.1	70.9	12	45.1	42.7	38
49	50	46.9	84	51.7	49.9	53
50	88	84.2	20	36	34.6	97
51	11.8	11.3	20	66.8	65	45
52	69.5	69	90	54.5	50.2	31
53	63	62.6	35	33	33	44
54	60	58.1	46	11.4	10.8	92
55	66.7	66.1	47	59.7	57.9	49
56	58	55.5	51	84.2	80.1	52
57	67.2	62.7	96	48.2	43.4	101
58	74.9	70.4	59	68.9	64.9	14
59	71.4	70.2	14	60.4	59.9	98
60	71.1	67.8	75	87.1	85.1	90
61	54	54	52	68.3	66.4	61
62	19.9	17.2	60	8.9	7.5	32
63	49.5	48.6	56	39.5	39.3	48
64	56.8	54.8	11	57.8	53.1	29
65	74	71.3	71	59	57.5	98
66	20.4	17	31	22.4	19.4	6
67	34.5	32.5	40	78.5	77.3	6
68	17.2	14.4	29	11.2	9.4	83
69	45	42.5	72	86.2	82	79
70	82	81	32	4	3.5	70
71	40	39.3	21	22.6	21.1	38
72	16	12.4	62	36	36	18
73	25	20.1	72	88	87.1	26
74	64.1	61.5	10	88.1	85.2	41
75	39.5	35.4	71	66.5	61.8	100
76	72	67.3	97	4.1	3.1	7
77	13	10.4	80	22	20.6	11
78	37.1	36.1	26	71.1	70.5	33
79	67.7	62.7	29	36.7	33.5	42
80	40	36.6	28	69.2	66.3	9
81	55.9	52.8	71	14.9	12.6	94
82	51	47.4	81	81	78.8	104
83	50	45.4	41	46.9	44.3	25
84	44.2	41	15	11.2	6.6	69
85	12	9.8	31	7	5.3	66
86	72	70	78	36	31.9	52
87	51.6	46.6	84	49.6	46.8	39
88	54.4	52.6	26	42.4	38.3	92
89	44.5	42.5	92	4.5	4	46
90	61.6	60.9	19	31.6	31	64
91	34.1	33.1	91	57.1	53.3	38
92	80	79	38	42	39	64
93	61.9	61.1	85	71.9	71	11
94	74.6	73.4	84	86.6	86.5	11
95	17	14.5	90	90	87.2	6
96	10.8	7.9	70	47.8	42.9	73
97	44.7	43.8	61	52.7	52.6	66
98	11.7	10.3	73	35.7	32	31
99	97.9	95.9	92	44.9	43.3	24
100	67.5	63	10	21.5	19.4	89
101	64	61.9	43	84.3	83.2	31
102	97.7	93.7	73	69.7	65.7	100
103	8.9	6.5	87	37.9	37.9	43
104	51.3	47.7	18	49.3	45.5	18
105	56	53.1	47	82.7	82.5	67
106	12.6	8.4	95	3.6	3.2	7
107	42.6	38.7	73	53.6	48.9	87
108	50	47.7	84	74.2	69.2	11
109	25.7	24.8	38	56.7	53.2	50
110	72.4	67.6	98	54.4	51	69
111	20.7	18.3	16	38.7	34	28
112	62.3	57.9	13	4.3	2.9	85
113	41.4	37.4	61	19.4	15.9	7
114	50	49	97	16.5	12.8	95
115	77.9	76.7	84	41.9	41	52
116	10	9.2	25	73	69.4	98
117	80	76.1	44	56	55.9	68
118	61.5	60	48	69.5	68.9	43
119	61.1	58.3	73	36.1	32.4	85
120	38.6	34.2	54	32.6	28	7
121	73.9	68.9	39	85.9	80.9	63
122	30	30	94	68.9	68.8	26
123	56	51.3	17	81.3	78.6	53
124	39	36.1	72	52	50.4	104
125	7.4	3.5	81	60.4	58.2	67
126	74.9	74.5	16	23.9	19.4	43
127	40	37.9	43	59.6	55.8	28
128	43	39	23	44.5	44.3	54
129	28.8	24.6	67	90.8	88.8	67
130	14.5	10.5	14	66.5	63.5	11
131	10.8	9.9	59	60.8	56	19
132	6.6	1.9	12	83.6	82.5	8
133	12.6	10.7	51	35.6	33.7	41
134	3.4	0.2	86	81.4	78.5	45
135	40.6	40.6	30	8.6	3.7	12
136	67	63.5	70	7.2	6.3	35
137	33.6	32	97	80.6	75.7	44
138	67	66	59	3.5	3.2	84
139	14	9.5	94	52	49.4	24
140	22.7	19.7	34	6.7	2.7	18
141	69.6	65.6	26	54.6	49.6	65
142	68.7	65.2	38	11.7	8.5	13
143	70	68	95	84.7	82.7	83
144	57	54	89	57.9	57.1	103
145	56.6	54.6	89	22.6	18.3	97
146	69.4	69.2	80	85.4	80.9	77
147	81.7	77.3	86	72.7	70.8	22
148	70	65.8	72	30.3	28.5	57
149	39.3	37.2	52	10.3	6.2	108
150	16.8	13.3	49	80.8	80.1	11
151	65.3	62.5	19	64.3	59.6	100
152	15.9	14	91	31.9	29	84
153	57.5	54.8	72	70.5	66.5	45
154	55.7	55	61	7.7	5.7	71
155	67.3	63.5	39	20.3	16.5	54
156	10	9.6	72	56	52.3	77
157	96	94.1	81	6	2.1	46
158	57.7	55.7	22	24.7	23.7	75
159	15.7	15.2	77	59.7	55.4	35
160	12.2	7.8	94	53.2	48.8	13
161	56.1	52.5	58	48.1	47.8	24
162	10.3	9.6	36	19.3	16.3	64
163	58	54.7	98	6.3	3.5	61
164	7.5	6.5	59	26.5	22	84
165	14.4	12.8	62	44.4	43.7	59
166	57.5	57.4	46	89.5	89.2	36
167	40.1	39.7	68	69.1	67.5	49
168	23.3	21	33	48.3	44.7	103
169	59	57.9	53	89	84.4	108
170	24.2	19.3	33	56.2	54.6	20
171	62	59.2	22	30	25.1	67
172	45	40.7	37	57.8	56.3	42
173	42	42	33	70.4	68.5	16
174	60	59.5	54	50.1	46.5	43
175	77.8	75	32	18.8	15.9	63
176	73	70	76	24	22.2	103
177	13.4	12	53	38.4	35.5	16
178	29	27.9	57	73.6	71.5	93
179	97	92.7	31	25	24.7	60
180	10	7.7	62	19	18.5	70
181	21.7	19.5	13	49.7	49.6	47
182	42.9	41.1	69	67.9	63.2	107
183	23	20	42	28.6	28.3	50
184	35	34.7	15	26.7	24.2	40
185	3.4	3.3	34	51.4	47	25
186	45	40.6	72	53.5	53.1	99
187	7.9	4.6	50	6.9	2.2	23
188	44	41.2	63	9.1	6.2	97
189	8	3.1	36	70	68.3	83
190	33	31.9	27	17	13	106
191	2.6	2.4	63	57.6	55.6	87
192	24	23	63	19.2	17.8	52
193	23.6	19.7	30	34.6	32.2	46
194	49.1	45.3	67	57.1	54.2	37
195	1.5	1.3	69	80.5	80.4	98
196	57.4	52.8	89	81.4	80.4	108
197	60.9	59.8	56	69.9	69	88
198	59.7	56.1	65	16.7	14.9	106
199	1.8	1.7	20	78.8	75.4	7
200	63.1	61.7	40	54.1	52.2	57

Expert Solution

Answre 6)

a) for Domestic cars

Standard Deviation (s) = 26.10928 (calculated from data given in table) ; Margin of Error (z)= 7

Z value at 98% confidence level = 2.33

We know that z = 2.33 * s / Where n is the sample size

Therefore n = (2.33 * s / z )² = (2.33 * 26.10928 / 7)² = 75.5276 ~76

Sample size required for Domestic cars = 76

b) for Foreign cars

Deviation (s) = 30.99688 (calculated from data given in table) ; Margin of Error (z)= 8

Z value at 98% confidence level = 2.33

We know that z = 2.33 * s / Where n is the sample size

Therefore n = (2.33 * s / z )² = (2.33 * 30.99688 / 8)² = 81.50191 ~82

Sample size required for Foreign cars = 82

Answer 7) a) Mean selling price of Domestic cars = 42396.5

Mean list price of Domestic cars = 44854

percent differnce = 42396.5/44854 = 94.5211

Selling price of 30000 worth domestic car = 30000*94.5211 = 28356.33

Average days for seling the domestic car = 53.29 ~ 53 days

b ) Mean selling price of Foreign cars = 44830

Mean list price of Foreign cars = 47228

percent differnce = 44830/47228 = 94.9225

Selling price of 30000 worth foreign car = 30000*94.9225 = 28476.75

Average days for seling the foreign car = 56.26 ~ 56 days

orchestra answered 2 years ago

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