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During the past year, Bubba's Burgers introduced a new dessert product into its Canadian market area. The product had already passed all the internal hurdles including focus groups and operational analysis, such as the time it takes to make and equipment constraints. The next step was to see how well the product would be received in the marketplace. In particular, Bubba's Burgers' Vice President for Production, Stephanie Linwood, was interested in estimating the mean number of orders for this dessert per 1,000 customer transactions. A random sample of 142 stores throughout Canada was selected. Store managers tracked the number of dessert orders per 1,000 transactions during a two-week trial period. See the file Bubba's Burgers
1. Based on these sample data construct and interpret a 95% confidence interval estimate for the mean number of dessert orders per 1,000 orders.
2. Suppose that Stephanie is not happy with the margin of error associated with the confidence interval estimate you found in question 1 and wants the margin of error to be no greater than +/-6 dessert orders per 1,000 customer orders. To meet this objective, how many more stores should be included in the sample? Alternatively, if Stephanie doesn't wish to increase the sample size, what other option is available to reduce the margin of error? Discuss the pros and cons of both approaches.
Sampled Store
Dessert Orders Per 1,000 Transactions
Store 1
185
Store 2
226
Store 3
290
Store 4
Store 5
255
Store 6
293
Store 7
138
Store 8
203
Store 9
276
Store 10
173
Store 11
275
Store 12
199
Store 13
213
Store 14
321
Store 15
97
Store 16
152
Store 17
319
Store 18
193
Store 19
126
Store 20
215
Store 21
186
Store 22
289
Store 23
181
Store 24
196
Store 25
183
Store 26
90
Store 27
178
Store 28
103
Store 29
Store 30
231
Store 31
158
Store 32
202
Store 33
234
Store 34
273
Store 35
218
Store 36
247
Store 37
223
Store 38
108
Store 39
238
Store 40
143
Store 41
206
Store 42
300
Store 43
89
Store 44
Store 45
250
Store 46
210
Store 47
137
Store 48
Store 49
204
Store 50
188
Store 51
Store 52
Store 53
123
Store 54
189
Store 55
Store 56
146
Store 57
136
Store 58
211
Store 59
164
Store 60
246
Store 61
324
Store 62
125
Store 63
195
Store 64
Store 65
179
Store 66
76
Store 67
248
Store 68
Store 69
Store 70
240
Store 71
224
Store 72
Store 73
222
Store 74
170
Store 75
147
Store 76
Store 77
207
Store 78
148
Store 79
Store 80
156
Store 81
Store 82
155
Store 83
201
Store 84
176
Store 85
111
Store 86
106
Store 87
232
Store 88
Store 89
Store 90
Store 91
242
Store 92
278
Store 93
Store 94
Store 95
225
Store 96
Store 97
309
Store 98
209
Store 99
Store 100
Store 101
190
Store 102
266
Store 103
256
Store 104
216
Store 105
230
Store 106
175
Store 107
127
Store 108
208
Store 109
Store 110
169
Store 111
91
Store 112
Store 113
Store 114
Store 115
Store 116
Store 117
Store 118
292
Store 119
151
Store 120
Store 121
132
Store 122
Store 123
241
Store 124
Store 125
239
Store 126
Store 127
205
Store 128
257
Store 129
Store 130
Store 131
Store 132
166
Store 133
Store 134
Store 135
Store 136
192
Store 137
145
Store 138
229
Store 139
304
Store 140
227
Store 141
139
Store 142
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