**Please only Use Excel/Handwritten calculations for this** Do not use R Studio.

The items for sale in many retail stores sometimes ring up at a different price at the cash register compared to the price marked on the shelf. This goes unnoticed by many consumers. But whether the mistakes are intentional or not, the retailers get checked by government inspectors (for overcharges only) and can potentially be fined for the mistakes if their error rate is high enough. The retailers also run the risk of receiving bad publicity through the press. As an example, in one such inspection: "during Walmart's second inspection, the price of a ceiling fan was off by $30. The shelf price listed the fan at $19.99, but it rang up as $49.97 at the register." For more, read: Inspector: One in 10 NC stores ring up wrong prices1. To avoid the fine and the public embarrassment that follows for being caught, each retailer will self-inspect their records. They typically use the same process as the government inspectors by selecting a random sample of items for cross-checking the register and the shelf prices. In a recent self-check, the store manager had her employees compare prices on 230 different items which were picked at random for cross-check. The employees recorded the shelf price and the price that appeared on the cash register. You can find these results in the MS Excel file titled "Price-Check". The government inspector will not fine companies that have an error rate of less than 2%.

Question 1 Based on the data in this study, what is the estimate of proportion of items that will ring up at higher prices and thus be counted as a violation? (Hint: Should your estimate be a single number or a range to provide appropriate background for managerial decision-making?) Question 2 Based on your answer for Question 1, if an inspector showed up today, would the store manager be 95% confident that the store will pass? Why, or why not? Question 3 If the manager wants to have a margin error of 0.5% (.005), then how many items need to be cross-checked?

Question 4 The manager doesn't believe she has the resources to do as many cross-checks to ensure a margin of error of 0.5%. She has noticed that in the items checked, some items are ringing up for less at the cash register, so technically, a customer could end up with a bill that is less than what they were expecting. She wonders if she would be able to defend her store against fines based on the average amount customers are being wrongly charged (either over- or undercharged). (Hint: for the purpose of this question, consider that items that ring up at correct prices essentially have the incorrect charge equal to zero. This is valuable data, and such items should be included in your calculation of the mean dollar amount of incorrect charges in Part (b)). a. Based on the collected sample data, what is the maximum overcharge for an item in this study? And what is the maximum undercharge for an item in this study? Insert answer here. b. Based on the collected sample data, what is the 95% confidence interval for the mean dollar amount of incorrect charges? Insert answer here. c. If the inspector's sample results in an error rate of 2.7% of items being overcharged, do you think showing the average error (accounting for both undercharges and overcharges) will help her avoid getting fined? Insert answer here. d. Should the store manager decides to do a larger study to be sure she can pass inspection? The fine for not passing an inspection is about $1,000, followed by a repeated inspection (as the recent news article tells us, "Walmart on New Hope Church Road in Raleigh, for example, failed three consecutive inspections, ringing up almost $5,000 in fines before finally passing." See Inspector: One in 10 NC stores ring up wrong prices). Please explain your answer.

Item	Shelf Price	Price at the Register
1	30,60	30,60
2	26,90	26,90
3	21,60	21,60
4	43,60	43,60
5	25,99	25,99
6	3,60	3,60
7	7,50	7,50
8	10,25	10,25
9	24,50	24,50
10	12,00	12,00
11	15,90	15,90
12	24,49	24,49
13	56,89	56,89
14	9,25	9,25
15	68,00	68,00
16	33,00	33,00
17	5,00	5,00
18	39,89	39,89
19	5,50	5,50
20	24,85	24,85
21	4,50	4,75
22	19,90	19,90
23	35,89	35,89
24	33,60	33,60
25	4,70	4,70
26	41,50	41,50
27	25,50	25,50
28	17,50	17,50
29	38,00	38,00
30	4,80	4,80
31	37,75	37,75
32	16,85	16,85
33	52,89	52,89
34	65,30	65,30
35	68,25	68,25
36	3,50	3,50
37	48,60	48,60
38	63,49	61,99
39	25,75	25,75
40	3,80	3,80
41	1,90	1,90
42	43,35	43,35
43	26,10	26,10
44	19,89	19,89
45	34,00	34,00
46	24,99	24,99
47	12,85	12,85
48	14,90	14,90
49	52,90	52,90
50	9,50	9,50
51	11,00	11,00
52	25,75	25,75
53	40,00	40,00
54	30,90	30,90
55	9,99	9,99
56	20,99	20,99
57	45,99	45,99
58	2,00	2,00
59	7,99	6,99
60	75,30	75,30
61	25,50	25,50
62	2,70	2,70
63	2,99	2,99
64	4,90	4,90
65	73,60	73,60
66	28,60	28,60
67	59,30	59,30
68	50,89	50,89
69	24,99	24,99
70	6,99	6,99
71	58,49	58,49
72	11,85	11,85
73	2,70	2,70
74	53,30	53,30
75	30,00	30,00
76	20,99	20,99
77	3,90	3,90
78	20,30	20,30
79	39,60	39,60
80	75,89	75,89
81	1,90	1,90
82	42,49	42,49
83	26,00	26,00
84	33,50	33,50
85	19,90	19,90
86	40,89	40,89
87	25,60	25,60
88	46,10	46,10
89	13,99	13,99
90	1,99	1,99
91	63,50	63,50
92	44,60	44,60
93	55,25	55,25
94	40,30	40,30
95	5,20	5,20
96	24,35	24,35
97	2,80	4,50
98	36,90	36,90
99	57,89	57,89
100	39,35	39,35
101	13,99	13,99
102	64,90	64,90
103	28,50	28,50
104	42,40	42,40
105	17,90	17,90
106	2,99	2,99
107	4,20	4,20
108	5,00	5,00
109	38,60	38,60
110	23,00	23,00
111	19,40	19,40
112	5,90	5,90
113	20,90	20,90
114	44,99	44,99
115	18,99	18,99
116	4,60	4,60
117	5,30	5,30
118	17,00	17,00
119	12,35	12,35
120	51,60	51,60
121	36,99	36,99
122	3,50	3,50
123	42,40	42,40
124	48,50	48,50
125	9,00	9,00
126	34,99	34,99
127	13,40	13,40
128	15,50	15,50
129	16,99	16,99
130	5,50	5,50
131	11,00	11,00
132	38,99	38,99
133	19,89	19,89
134	21,40	21,40
135	34,90	34,90
136	32,90	32,90
137	8,99	8,99
138	8,89	8,89
139	9,30	9,30
140	9,50	9,50
141	25,50	25,50
142	16,40	16,40
143	29,50	29,50
144	24,99	24,99
145	18,25	18,25
146	20,60	20,60
147	5,89	5,89
148	6,25	6,25
149	6,89	6,89
150	24,00	24,00
151	35,25	35,25
152	32,4	32,4
153	5,25	5,25
154	4,3	4,3
155	34,6	34,6
156	14,25	14,25
157	17,25	17,25
158	20,3	20,3
159	22,9	22,9
160	26,5	26,5
161	33,89	33,89
162	28,6	28,6
163	9,5	9,5
164	36,99	36,99
165	13,3	13,3
166	35	35
167	35,25	35,25
168	9,89	9,89
169	16,25	16,25
170	29,99	29,99
171	21,89	21,89
172	36,89	36,89
173	16,6	16,6
174	10,3	10,3
175	13,8	13,8
176	11,5	11,5
177	18,6	18,6
178	10	10
179	12,25	12,25
180	15,99	15,99
181	37,4	37,4
182	31,6	31,6
183	17,5	17,5
184	30,8	30,8
185	10,25	10,25
186	24	24
187	9,99	9,99
188	29,99	29,99
189	37,25	37,25
190	20,89	20,89
191	23	23
192	36,99	36,99
193	4,99	4,99
194	33,5	33,5
195	18,5	18,5
196	31	31
197	35,3	35,3
198	10,99	10,99
199	11,5	11,5
200	22,3	22,3
201	12,00	12,00
202	17,30	17,30
203	17,90	17,90
204	15,40	15,40
205	7,40	7,40
206	18,20	18,20
207	16,20	17,99
208	10,70	10,70
209	10,10	10,10
210	15,50	15,50
211	19,90	19,90
212	8,60	8,60
213	17,20	17,20
214	14,60	14,60
215	14,60	14,60
216	9,50	9,50
217	12,40	12,40
218	11,00	11,00
219	16,60	16,60
220	7,40	7,40
221	12,90	12,90
222	8,10	8,10
223	7,80	7,80
224	14,20	14,20
225	13,10	13,10
226	16,80	16,80
227	12,30	12,30
228	19,30	19,30
229	16,40	16,40
230	12,90	12,90