Business Statistics 8th ed. Chapter 8 - Case study 2 - Federal Aviation Administ
ID: 3217419 • Letter: B
Question
Business Statistics 8th ed. Chapter 8 - Case study 2 - Federal Aviation Administration.
In January 2003, the FAA ordered that passengers be weighed before boarding 10- to 19- seat passenger planes. The order was instituted in response to a crash that occurred on January 8, 2003, in Charlotte, North Carolina, in which all 21 passengers, including the pilot and copilot, of a 19-seat Beech 1900 turboprop died. One possible cause of the crash was that the plane may have been carrying too much weight.
The airlines were asked to weigh adult passengers and carry-on bags randomly over a one-month period to estimate the mean weight per passenger (including luggage). A total of 426 people and their luggage were weighed, and the same data are contained in a data file called FAA.
a) Prepare a descriptive analysis of the data using charts, graphs, and numerical measures. (DONE)
b) Construct and interpret a 95% confidence interval estimate for the mean weight for male passengers. (DONE)
c)Construct and interpret a 95% confidence interval estimate for the mean weight for female passengers. (DONE)
d)Construct and interpret a 95% confidence interval estimate for the mean weight for all passengers.(DONE)
e)Indicate what sample size would be required if the margin of error in the estimate for the mean of all passengers is to be reduced by half.
Questions a-d are solved. Just need question e.
Here is the data below:
Weight Gender Age
197 Male 55
171 Male 47
212 Male 62
239 Male 49
237 Male 36
252 Male 47
146 Male 46
199 Male 47
235 Male 52
176 Male 62
186 Male 56
159 Male 51
155 Male 67
179 Male 51
184 Male 56
148 Male 44
190 Male 53
194 Male 52
209 Male 55
195 Male 50
196 Male 51
195 Male 54
241 Male 47
203 Male 59
200 Male 57
191 Male 58
258 Male 52
228 Male 57
269 Male 50
187 Male 54
250 Male 42
161 Male 53
220 Male 50
229 Male 61
257 Male 42
203 Male 53
191 Male 48
223 Male 50
195 Male 44
225 Male 53
166 Male 64
182 Male 52
164 Male 65
195 Male 47
204 Male 51
206 Male 49
196 Male 55
264 Male 47
158 Male 61
185 Male 52
135 Male 70
244 Male 52
170 Male 50
187 Male 53
225 Male 55
218 Male 58
229 Male 49
221 Male 48
168 Male 53
175 Male 68
224 Male 45
214 Male 51
180 Male 56
198 Male 56
209 Male 53
220 Male 56
209 Male 47
180 Male 56
256 Male 53
218 Male 59
207 Male 54
227 Male 58
228 Male 48
188 Male 65
180 Male 55
235 Male 44
173 Male 47
163 Male 48
224 Male 46
222 Male 47
265 Male 49
244 Male 65
240 Male 55
208 Male 43
205 Male 56
217 Male 46
204 Male 60
177 Male 49
157 Male 49
227 Male 55
217 Male 59
222 Male 40
211 Male 43
177 Male 51
238 Male 55
197 Male 73
182 Male 48
183 Male 45
193 Male 61
193 Male 49
191 Male 42
228 Male 46
219 Male 43
189 Male 61
240 Male 62
157 Male 55
220 Male 43
202 Male 66
206 Male 57
187 Male 47
190 Male 62
228 Male 50
227 Male 50
217 Male 51
224 Male 65
249 Male 46
213 Male 51
221 Male 54
255 Male 51
196 Male 49
233 Male 53
209 Male 41
236 Male 62
201 Male 53
184 Male 48
234 Male 51
189 Male 62
219 Male 38
220 Male 60
196 Male 44
193 Male 40
168 Male 55
259 Male 60
190 Male 45
207 Male 50
199 Male 55
282 Male 56
239 Male 50
229 Male 47
241 Male 52
210 Male 54
220 Male 62
198 Male 34
172 Male 49
239 Male 59
197 Male 52
170 Male 60
226 Male 53
226 Male 54
217 Male 56
216 Male 54
188 Male 47
225 Male 53
219 Male 54
234 Male 51
130 Male 56
218 Male 58
245 Male 56
158 Male 43
206 Male 55
242 Male 56
251 Male 56
211 Male 40
209 Male 38
255 Male 59
204 Male 72
187 Male 54
229 Male 44
205 Male 53
233 Male 57
217 Male 46
244 Male 42
202 Male 73
179 Male 58
163 Male 50
136 Male 59
208 Male 56
213 Male 57
205 Male 57
210 Male 54
212 Male 57
245 Male 54
207 Male 60
175 Male 48
167 Male 50
210 Male 65
231 Male 45
164 Male 44
189 Male 48
219 Male 46
199 Male 61
196 Male 54
201 Male 52
193 Male 48
183 Male 57
222 Male 61
207 Male 61
239 Male 49
212 Male 54
207 Male 59
211 Male 48
211 Male 47
205 Male 48
172 Male 53
211 Male 66
209 Male 49
225 Male 44
185 Male 51
222 Male 45
211 Male 46
208 Male 46
228 Male 51
254 Male 50
170 Male 50
172 Male 58
220 Male 60
237 Male 54
181 Male 58
147 Male 55
181 Male 43
210 Male 36
217 Male 48
178 Male 58
182 Male 56
217 Male 43
208 Male 55
190 Male 41
208 Male 60
180 Male 60
181 Male 53
233 Male 55
249 Male 59
187 Male 49
200 Male 47
208 Male 51
255 Male 61
221 Male 52
250 Male 56
210 Male 40
247 Male 58
188 Male 48
179 Male 67
237 Male 47
230 Male 49
158 Male 64
239 Male 57
200 Male 53
174 Male 49
154 Male 35
183 Male 45
218 Male 57
230 Male 65
203 Male 53
204 Male 46
211 Male 60
195 Male 50
230 Male 48
192 Male 49
268 Male 60
225 Male 37
221 Male 61
179 Male 47
229 Male 45
244 Male 48
185 Male 58
197 Male 65
169 Male 55
242 Male 38
233 Male 63
210 Male 39
146 Male 49
219 Male 65
219 Male 54
238 Male 44
179 Male 52
238 Male 68
190 Male 48
185 Male 60
158 Male 41
242 Male 48
179 Male 50
247 Male 46
173 Male 52
194 Male 62
170 Male 40
248 Male 34
206 Male 56
214 Male 44
231 Male 55
258 Male 46
203 Male 59
177 Male 47
190 Male 47
228 Male 44
229 Male 44
219 Male 59
165 Male 62
167 Male 51
201 Male 56
188 Male 53
188 Male 53
229 Male 43
182 Male 59
202 Male 57
199 Male 59
246 Male 56
169 Male 49
180 Male 50
200 Male 54
176 Male 43
166 Male 53
147 Male 35
221 Male 46
196 Male 59
216 Male 44
150 Male 48
237 Male 47
152 Male 59
191 Male 45
179 Male 49
202 Male 49
209 Male 46
252 Male 52
191 Male 53
184 Male 27
185 Male 33
221 Male 51
240 Male 35
166 Male 33
231 Male 46
248 Male 30
187 Male 38
207 Male 40
183 Male 45
224 Male 46
211 Male 42
206 Male 54
177 Male 52
197 Male 29
225 Male 35
205 Male 45
232 Male 30
178 Male 27
225 Male 41
239 Male 28
146 Female 47
131 Female 45
139 Female 37
152 Female 45
139 Female 42
117 Female 37
123 Female 31
138 Female 36
109 Female 36
128 Female 35
123 Female 47
121 Female 32
171 Female 37
127 Female 48
96 Female 36
139 Female 37
130 Female 45
127 Female 28
160 Female 45
152 Female 48
164 Female 29
90 Female 39
107 Female 32
134 Female 27
108 Female 36
110 Female 33
114 Female 48
143 Female 31
168 Female 36
140 Female 43
135 Female 40
148 Female 43
160 Female 44
102 Female 37
154 Female 37
128 Female 37
144 Female 44
145 Female 36
120 Female 24
159 Female 47
135 Female 43
127 Female 55
136 Female 46
147 Female 41
157 Female 58
112 Female 57
133 Female 47
103 Female 43
156 Female 45
122 Female 52
159 Female 47
108 Female 73
171 Female 50
122 Female 55
163 Female 47
148 Female 53
159 Female 48
127 Female 50
132 Female 53
136 Female 55
123 Female 62
135 Female 55
128 Female 50
142 Female 60
116 Female 48
113 Female 48
124 Female 55
122 Female 48
155 Female 57
149 Female 49
113 Female 52
139 Female 59
182 Female 44
137 Female 70
115 Female 61
115 Female 58
152 Female 48
116 Female 58
93 Female 51
140 Female 49
103 Female 54
Explanation / Answer
e)Indicate what sample size would be required if the margin of error in the estimate for the mean of all passengers is to be reduced by half.
Here we have to find sample size (n)
The formula for sample size is,
n = [(Zc*s) /E]
Here s is standard deviation of the data.
E is margin of error =1/2= 0.5
Zc is the critical value for normal distribution.
Zc we can find by using EXCEL.
syntax :
=NORMSINV(probability)
where probability = 1 - a/2
a = 1 - C
Here confidence level C = 95% = 0.95
a = 1 - C
Zc = 1.96
s = 38.87
n = [ (1.96*38.87) / 0.5]2 = 23215.64
ANd if C = 0.99 then
Zc = 2.58
n = [ (2.58*38.87) / 0.5]2 = 40097.62
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