Please give me right answers.. You may use Minitab or other software for any cal
ID: 3173621 • Letter: P
Question
Please give me right answers..
You may use Minitab or other software for any calculations. However, you must show your
manual calculations unless indicated otherwise. You may paste your output onto your
assignment to show your use of Minitab; however, this output does not replace any of the steps
outlined below. This means that answers that are exclusively Minitab output may receive only
one mark.
Question 4 - Consumer Perceptions of Food Safety
Vendors of prepared food are very sensitive to the public’s perception of the safety of the food they
sell. Food sold at outdoor fairs and festivals may be less safe than food sold in restaurants because it is
prepared in temporary locations and often by volunteer help. What do people who attend fairs think
about the safety of the food served? One study asked the following question to people at a number of
fairs:
How often do you think people become sick because of food they consume prepared at outdoor fairs
and festivals?
The possible responses were:
1 = very rarely
2 = once in a while
3 = often
4 = more often than not
5 = always
In all, 303 people answered this question.
The dataset FoodSafety includes the following variables: subject, sfair, srest, and gender. The variable
“sfair” contains the responses concerning safety of food served at outdoor fairs and festivals. The
variable “srest” contains responses to the same question asked about food served in restaurants.
a) Is there good evidence that men and women differ in their perceptions about food safety at fairs? Is
this true for restaurants? Select an appropriate nonparametric test and use Minitab to obtain your
results. Explain your conclusions.
b) Now you wonder if people are more concerned about the safety of food served at fairs than they are
about the safety of food served at restaurants. Explain carefully why we cannot answer this question
by applying the Wilcoxon Rank-Sum Test (a.k.a. the Mann-Whitney Test) to the variables “sfair”
and “srest”.
c) We suspect that restaurant food will appear safer than food served outdoors at a fair. Do the data
give good evidence for this suspicion? Use Minitab to perform an appropriate nonparametric test
and report your findings. Provide a p-value and your conclusion.
minitab data below..
subject
hfair
sfair
sfast
srest
gender
1 4 1 1 1 Woman
2 4 2 4 2 Woman
3 2 2 2 2 Woman
4 4 2 2 1 Woman
5 2 3 1 3 Woman
6 1 2 2 2 Woman
7 1 3 2 2 Woman
8 4 2 4 4 Woman
9 1 2 3 2 Woman
10 2 2 2 2 Woman
11 4 2 2 2 Woman
12 1 2 2 1 Woman
13 1 2 2 1 Woman
14 4 2 2 2 Woman
15 2 2 2 2 Man
16 2 2 2 2 Man
17 1 1 1 1 Man
18 2 2 2 2 Man
19 2 2 2 1 Man
20 2 2 4 3 Man
21 2 2 2 2 Man
22 4 1 1 1 Man
23 3 2 2 1 Man
24 2 2 1 1 Man
25 4 2 3 2 Man
26 1 3 3 2 Woman
27 4 2 3 2 Man
28 1 2 2 1 Man
29 2 2 2 2 Man
30 4 1 1 1 Man
31 2 2 1 1 Man
32 2 1 3 2 Man
33 1 2 3 2 Woman
34 2 4 4 3 Woman
35 2 2 2 1 Woman
36 4 2 2 2 Woman
37 3 1 1 1 Woman
38 4 2 2 1 Woman
39 1 2 2 1 Woman
40 1 3 3 1 Woman
41 1 2 2 1 Woman
42 1 2 2 2 Woman
43 2 2 1 1 Woman
44 2 2 2 2 Woman
45 4 1 2 1 Woman
46 3 1 2 1 Woman
47 1 2 2 2 Woman
48 3 2 4 1 Woman
49 3 1 1 1 Woman
50 2 2 4 1 Woman
51 3 1 1 1 Man
52 1 1 1 1 Man
53 4 2 2 2 Woman
54 2 2 2 2 Woman
55 2 4 2 2 Woman
56 4 2 2 2 Woman
57 2 3 2 2 Woman
58 3 2 1 1 Man
59 2 2 2 2 Woman
60 2 3 2 2 Woman
61 3 2 3 2 Woman
62 4 3 2 3 Man
63 1 2 4 3 Woman
64 2 4 3 3 Woman
65 2 2 2 2 Woman
66 1 2 2 2 Woman
67 2 4 2 1 Woman
68 2 1 2 1 Man
69 3 2 2 2 Man
70 3 3 4 2 Man
71 3 1 1 1 Man
72 3 2 2 1 Man
73 2 1 1 1 Man
74 3 3 2 2 Man
75 4 1 2 1 Man
76 1 4 2 2 Man
77 1 1 1 1 Man
78 2 2 2 2 Woman
79 2 2 2 2 Woman
80 4 2 3 1 Woman
81 1 3 3 3 Woman
82 4 2 3 3 Woman
83 3 2 2 2 Woman
84 2 2 2 2 Woman
85 3 2 2 1 Man
86 2 2 2 1 Woman
87 2 3 3 2 Woman
88 1 2 2 2 Man
89 1 3 3 2 Woman
90 3 2 2 2 Woman
91 1 2 2 2 Woman
92 1 3 1 1 Woman
93 3 2 2 2 Woman
94 3 1 2 1 Woman
95 1 1 3 2 Woman
96 2 2 3 2 Woman
97 2 3 4 1 Woman
98 1 2 2 2 Woman
99 4 2 2 1 Woman
100 1 3 3 2 Woman
101 2 4 4 3 Woman
102 3 1 2 2 Woman
103 1 2 2 1 Woman
104 3 3 1 5 Man
105 3 1 2 1 Man
106 3 2 2 1 Man
107 2 2 2 1 Man
108 1 2 2 2 Man
109 1 5 2 1 Man
110 1 4 2 2 Man
111 2 2 2 1 Man
112 1 4 2 1 Man
113 1 2 1 1 Man
114 4 3 5 5 Man
115 2 2 2 2 Man
116 2 3 3 1 Man
117 2 3 3 2 Man
118 3 2 3 2 Man
119 2 2 2 1 Man
120 2 2 3 2 Man
121 2 3 3 2 Woman
122 1 3 2 2 Woman
123 1 3 2 2 Man
124 1 3 3 3 Woman
125 1 2 2 2 Woman
126 2 2 2 2 Woman
127 1 3 4 1 Woman
128 2 2 2 2 Woman
129 1 2 3 2 Woman
130 3 2 1 1 Woman
131 1 2 2 2 Woman
132 1 2 2 1 Man
133 1 2 2 1 Man
134 3 2 2 2 Man
135 1 2 3 1 Man
136 4 1 2 1 Man
137 1 1 4 2 Man
138 1 3 2 2 Woman
139 4 3 3 2 Woman
140 1 1 1 1 Man
141 1 1 2 2 Man
142 2 3 3 2 Woman
143 1 2 2 2 Woman
144 1 2 2 1 Woman
145 4 3 2 2 Woman
146 1 3 2 2 Woman
147 2 4 3 2 Woman
148 3 1 2 1 Woman
149 4 2 2 1 Woman
150 4 1 1 1 Man
151 3 3 2 2 Man
152 2 3 3 1 Man
153 1 2 2 1 Man
154 3 1 1 1 Man
155 2 2 2 2 Woman
156 4 5 2 2 Woman
157 1 2 2 2 Woman
158 3 3 3 2 Woman
159 1 4 3 2 Woman
160 2 2 2 2 Woman
161 1 2 2 2 Woman
162 2 2 2 2 Woman
163 1 4 2 1 Woman
164 1 2 3 2 Woman
165 2 2 2 2 Woman
166 2 2 3 3 Man
167 2 3 1 1 Man
168 1 2 3 1 Woman
169 1 3 3 2 Woman
170 4 3 3 3 Woman
171 2 1 1 1 Woman
172 1 3 2 2 Man
173 1 2 1 1 Man
174 1 1 1 1 Man
175 1 4 3 2 Woman
176 2 4 2 2 Woman
177 1 3 3 3 Woman
178 2 2 2 2 Woman
179 1 4 4 2 Woman
180 4 2 2 1 Man
181 1 2 2 2 Woman
182 3 2 2 2 Woman
183 1 4 4 2 Woman
184 1 3 2 1 Woman
185 3 2 2 2 Woman
186 1 4 4 1 Woman
187 1 4 2 2 Woman
188 4 2 4 2 Woman
189 3 3 2 2 Woman
190 2 3 3 2 Woman
191 2 2 2 2 Man
192 2 2 1 1 Man
193 2 3 3 3 Man
194 1 2 2 2 Man
195 2 2 3 2 Man
196 2 2 2 2 Man
197 1 3 2 2 Woman
198 1 4 2 2 Man
199 2 4 3 2 Woman
200 3 2 2 2 Man
201 1 4 2 1 Woman
202 3 2 4 4 Woman
203 2 2 2 2 Woman
204 2 3 3 3 Woman
205 2 3 2 2 Woman
206 2 3 3 2 Man
207 2 2 2 2 Woman
208 1 1 2 1 Woman
209 2 2 3 2 Woman
210 2 2 2 2 Woman
211 3 2 2 2 Woman
212 2 3 4 2 Woman
213 1 4 4 2 Man
214 2 2 2 2 Man
215 2 2 2 2 Woman
216 2 3 3 3 Woman
217 1 3 2 2 Man
218 2 2 1 1 Woman
219 3 3 3 2 Woman
220 4 3 2 2 Woman
221 2 2 2 1 Man
222 2 3 3 2 Woman
223 3 2 2 2 Woman
224 1 2 3 2 Woman
225 1 3 3 3 Woman
226 4 1 1 1 Woman
227 3 2 2 1 Woman
228 2 2 2 1 Woman
229 4 1 1 1 Man
230 4 2 2 2 Woman
231 2 4 2 2 Woman
232 1 4 2 2 Woman
233 3 2 2 2 Man
234 3 2 3 2 Woman
235 4 2 2 2 Woman
236 1 3 2 2 Woman
237 2 2 4 2 Woman
238 1 3 3 3 Man
239 3 2 1 1 Man
240 1 3 3 2 Woman
241 1 2 2 2 Woman
242 2 4 4 4 Woman
243 2 2 2 2 Woman
244 2 3 2 3 Woman
245 1 2 1 1 Woman
246 1 2 2 2 Woman
247 2 2 2 2 Woman
248 2 4 2 5 Woman
249 2 2 2 2 Woman
250 2 3 2 2 Woman
251 2 2 2 2 Woman
252 2 2 3 1 Woman
253 2 4 4 4 Woman
254 1 2 2 2 Woman
255 4 2 2 2 Woman
256 1 2 2 1 Woman
257 2 2 1 1 Woman
258 4 3 1 1 Woman
259 1 3 2 2 Woman
260 2 4 2 2 Woman
261 1 1 3 2 Woman
262 5 1 1 1 Man
263 1 2 2 1 Man
264 2 3 2 1 Man
265 1 2 3 2 Man
266 1 3 3 3 Man
267 2 2 2 2 Man
268 3 2 2 1 Man
269 2 2 1 1 Man
270 3 2 2 2 Woman
271 3 2 2 2 Woman
272 2 2 2 1 Woman
273 2 2 2 1 Woman
274 1 2 2 1 Man
275 1 2 2 1 Man
276 4 3 2 3 Man
277 2 2 2 1 Man
278 2 3 3 3 Woman
279 1 3 2 2 Woman
280 4 2 2 2 Man
281 1 2 2 2 Woman
282 1 2 3 2 Man
283 3 2 2 2 Woman
284 2 2 3 2 Woman
285 3 2 3 2 Man
286 2 3 3 2 Man
287 2 2 2 2 Woman
288 2 2 3 3 Man
289 1 5 4 3 Woman
290 1 3 2 2 Woman
291 2 2 3 2 Woman
292 2 2 2 2 Woman
293 1 2 3 4 Woman
294 2 3 2 2 Man
295 2 2 2 3 Woman
296 2 2 2 3 Woman
297 2 3 2 2 Man
298 2 3 4 2 Woman
299 2 3 3 3 Woman
300 1 3 2 2 Woman
301 1 4 3 1 Woman
302 1 3 2 2 Woman
303 3 1 2 2 Man
subject
hfair
sfair
sfast
srest
gender
Explanation / Answer
I have used R-programming to do the given exercises as it was given that you may use Minitab or other software for any calculations
a) Is there good evidence that men and women differ in their perceptions about food safety at fairs? Is
this true for restaurants? Select an appropriate nonparametric test and use Minitab to obtain your
results. Explain your conclusions.
Created a dataframe "food" with the given data.
Ran the Kruskal-Wallis test (non-parametric test) to check evidence that men and women differ in their perceptions about food safety at fairs.
> head(food)
subject hfair sfair sfast srest gender
1 1 4 1 1 1 Woman
2 2 4 2 4 2 Woman
3 3 2 2 2 2 Woman
4 4 4 2 2 1 Woman
5 5 2 3 1 3 Woman
6 6 1 2 2 2 Woman
> kruskal.test(sfair ~ gender, data = food)
Kruskal-Wallis rank sum test
data: sfair by gender
Kruskal-Wallis chi-squared = 11.117, df = 1, p-value = 0.0008552
As the p-value of Kruskal-Wallis rank sum test (0.0008552) is less than the significance level of 0.05, we conclude that at 0.05 significance level, men and women differ in their perceptions about food safety at fairs.
For restaurant, we ran the below command.
> kruskal.test(srest ~ gender, data = food)
Kruskal-Wallis rank sum test
data: srest by gender
Kruskal-Wallis chi-squared = 14.547, df = 1, p-value = 0.0001367
As the p-value of Kruskal-Wallis rank sum test (0.0001367) is less than the significance level of 0.05, we conclude that at 0.05 significance level, men and women differ in their perceptions about food safety at restaurants.
b) Now you wonder if people are more concerned about the safety of food served at fairs than they are
about the safety of food served at restaurants. Explain carefully why we cannot answer this question
by applying the Wilcoxon Rank-Sum Test (a.k.a. the Mann-Whitney Test) to the variables “sfair”
and “srest”.
Using the Mann-Whitney-Wilcoxon Test, we can decide whether the two samples are identical without assuming them to follow the normal distribution. In this case where we need to compare the samples based on safety of food served at fairs than they are about the safety of food served at restaurants and both variables "sfair" and "srest" have 5 factor levels (1,2,3,4,5), the population will be divided into 5 different samples for different values of "sfair" or "srest". So, we cannot do Mann-Whitney-Wilcoxon Test as it compares only 2 samples. We get the below error in R, while running the below command.
> wilcox.test(sfair ~ srest, data=food)
Error in wilcox.test.formula(sfair ~ srest, data = food) :
grouping factor must have exactly 2 levels
c) We suspect that restaurant food will appear safer than food served outdoors at a fair. Do the data
give good evidence for this suspicion? Use Minitab to perform an appropriate nonparametric test
and report your findings. Provide a p-value and your conclusion.
We can use Kruskal-Wallis test (non-parametric test) to check evidence that restaurant food will appear safer than food served outdoors at a fair.
> kruskal.test(sfair ~ srest, data = food)
Kruskal-Wallis rank sum test
data: sfair by srest
Kruskal-Wallis chi-squared = 47.822, df = 4, p-value = 1.028e-09
As the p-value of Kruskal-Wallis rank sum test (1.028e-09) is less than the significance level of 0.05, we conclude that at 0.05 significance level, perceptions about food safety at fairs differ in perceptions about food safety at restaurants.