Part I: Statistical Measures
Statistics is a very powerful topic that is used on a daily basis in many situations. , you may be interested in the age of the men who attend Silver’s Gym. You could not assume that all men are the same age. Thus, it would be an inaccurate measure to state that “the average age of men who attend Silver’s Gym is the same age as me.”
Averages are only one type of statistical measurements that may be of interest. , your company likes to gauge sales during a certain time of year and to keep costs low to a point that the business is making money. These various statistical measurements are important in the world of statistics because they help you make general conclusions about a given population or sample.
To assist in your analysis ’s Gym, answer the following questions about the Body Fat Versus Weight data set:
Click here to download the Body Fat Weight data set.
Calculate the mean, median, range, and standard deviation Body Fat Versus Weight data set. Report your findings, and interpret the meanings of each measurement. Notice you are to calculate the mean, median, range, and standard deviation body fat and weight.
· The measures of central tendency are important in real-world situations.
o What is the importance of finding the mean/median? Why might you find this information useful?
In some data sets, the mean is more important than the median. , you want to know your mean overall grade average because the median grade average would be meaningless. However, you might be interested in a median salary to see the middle value of where salaries fall. Explain which measure, the mean or the median, is more applicable data set and this problem.
What is the importance of finding the range/standard deviation? Why might you find this information useful?
Part II: Hypothesis Testing
Organizations sometimes want to go beyond describing the data and actually perform some type of inference on the data. Hypothesis testing is a statistical technique that is used to help make inferences about a population parameter. Hypothesis testing allows you to test whether a claim about a parameter is accurate or not.
Your boss makes the claim that the average body fat in men attending Silver’s Gym is 20%. You believe that the average body fat attending Silver’s Gym is not 20%. such as this, you can set up a hypothesis test to reach one of two possible conclusions: either a decision cannot be made to disprove the body fat average of 20%, or there is enough evidence to say that the body fat average claim is inaccurate.
To assist in your analysis ’s Gym, consider the following steps based on your boss’s claim that the mean body fat in men attending Silver’s Gym is 20%:
First, construct the null and alternative hypothesis test based on the claim by your boss.
Using an alpha level of 0.05, perform a hypothesis test, and report your findings. Be sure to discuss which test you will be using and the reason . Recall you found the body fat mean and standard deviation in Part I of the task.
Based on your results, interpret the final decision to report to your boss.
IDNO
BODYFAT
WEIGHT
1
12.6
154.25
2
6.9
173.25
3
24.6
154.00
4
10.9
184.75
5
27.8
184.25
6
20.6
210.25
7
19.0
181.00
8
12.8
176.00
9
5.1
191.00
10
12.0
198.25
11
7.5
186.25
12
8.5
216.00
13
20.5
180.50
14
20.8
205.25
15
21.7
187.75
16
20.5
162.75
17
28.1
195.75
18
22.4
209.25
19
16.1
183.75
20
16.5
211.75
21
19.0
179.00
22
15.3
200.50
23
15.7
140.25
24
17.6
148.75
25
14.2
151.25
26
4.6
159.25
27
8.5
131.50
28
22.4
148.00
29
4.7
133.25
30
9.4
160.75
31
12.3
182.00
32
6.5
160.25
33
13.4
168.00
34
20.9
218.50
35
31.1
247.25
36
38.2
191.75
37
23.6
202.25
38
27.5
196.75
39
33.8
363.15
40
31.3
203.00
41
33.1
262.75
42
31.7
205.00
43
30.4
217.00
44
30.8
212.00
45
8.4
125.25
46
14.1
164.25
47
11.2
133.50
48
6.4
148.50
49
13.4
135.75
50
5.0
127.50
51
10.7
158.25
52
7.4
139.25
53
8.7
137.25
54
7.1
152.75
55
4.9
136.25
56
22.2
198.00
57
20.1
181.50
58
27.1
201.25
59
30.4
202.50
60
24.0
179.75
61
25.4
216.00
62
28.8
178.75
63
29.6
193.25
64
25.1
178.00
65
31.0
205.50
66
28.9
183.50
67
21.1
151.50
68
14.0
154.75
69
7.1
155.25
70
13.2
156.75
71
23.7
167.50
72
9.4
146.75
73
9.1
160.75
74
13.7
125.00
75
12.0
143.00
76
18.3
148.25
77
9.2
162.50
78
21.7
177.75
79
21.1
161.25
80
18.6
171.25
81
30.2
163.75
82
26.0
150.25
83
18.2
190.25
84
26.2
170.75
85
26.1
168.00
86
25.8
167.00
87
15.0
157.75
88
22.6
160.00
89
8.8
176.75
90
14.3
176.00
91
20.2
177.00
92
18.1
179.75
93
9.2
165.25
94
24.2
192.50
95
9.6
184.25
96
17.3
224.50
97
10.1
188.75
98
11.1
162.50
99
17.7
156.50
100
21.7
197.00
101
20.8
198.50
102
20.1
173.75
103
19.8
172.75
104
21.9
196.75
105
24.7
177.00
106
17.8
165.50
107
19.1
200.25
108
18.2
203.25
109
17.2
194.00
110
21.0
168.50
111
19.5
170.75
112
27.1
183.25
113
21.6
178.25
114
20.9
163.00
115
25.9
175.25
116
16.7
158.00
117
19.8
177.25
118
14.1
179.00
119
25.1
191.00
120
17.9
187.50
121
27.0
206.50
122
24.6
185.25
123
14.8
160.25
124
16.0
151.50
125
14.0
161.00
126
17.4
167.00
127
26.4
177.50
128
17.4
152.25
129
20.4
192.25
130
15.0
165.25
131
18.0
171.75
132
22.2
171.25
133
23.1
197.00
134
25.3
157.00
135
23.8
168.25
136
26.3
186.00
137
21.4
166.75
138
28.4
187.75
139
21.8
168.25
140
20.1
212.75
141
24.3
176.75
142
18.1
173.25
143
22.7
167.00
144
9.9
159.75
145
10.8
188.15
146
14.4
156.00
147
19.0
208.50
148
28.6
206.50
149
6.1
143.75
150
24.5
223.00
151
9.9
152.25
152
19.1
241.75
153
10.6
146.00
154
16.5
156.75
155
20.5
200.25
156
17.2
171.50
157
30.1
205.75
158
10.5
182.50
159
12.8
136.50
160
22.0
177.25
161
9.9
151.25
162
14.8
196.00
163
13.3
184.25
164
15.2
140.00
165
26.5
218.75
166
19.0
217.00
167
21.4
166.25
168
20.0
224.75
169
34.7
228.25
170
16.5
172.75
171
4.1
152.25
172
1.9
125.75
173
20.2
177.25
174
16.8
176.25
175
24.6
226.75
176
10.4
145.25
177
13.4
151.00
178
28.8
241.25
179
22.0
187.25
180
16.8
234.75
181
25.8
219.25
182
0.0
118.50
183
11.9
145.75
184
12.4
159.25
185
17.4
170.50
186
9.2
167.50
187
23.0
232.75
188
20.1
210.50
189
20.2
202.25
190
23.8
185.00
191
11.8
153.00
192
36.5
244.25
193
16.0
193.50
194
24.0
224.75
195
22.3
162.75
196
24.8
180.00
197
21.5
156.25
198
17.6
168.00
199
7.3
167.25
200
22.6
170.75
201
12.5
178.25
202
21.7
150.00
203
27.7
200.50
204
6.8
184.00
205
33.4
223.00
206
16.6
208.75
207
31.7
166.00
208
31.5
195.00
209
10.1
160.50
210
11.3
159.75
211
7.8
140.50
212
26.4
216.25
213
19.3
168.25
214
18.5
194.75
215
19.3
172.75
216
45.1
219.00
217
13.8
149.25
218
8.2
154.50
219
23.9
199.25
220
15.1
154.50
221
12.7
153.25
222
25.3
230.00
223
11.9
161.75
224
6.1
142.25
225
11.3
179.75
226
12.8
126.50
227
14.9
169.50
228
24.5
198.50
229
15.0
174.50
230
16.9
167.75
231
11.1
147.75
232
16.1
182.25
233
15.5
175.50
234
25.9
161.75
235
25.5
157.75
236
18.4
168.75
237
24.0
191.50
238
26.4
219.15
239
12.7
155.25
240
28.8
189.75
241
17.0
127.50
242
33.6
224.50
243
29.3
234.25
244
31.4
227.75
245
28.1
199.50
246
15.3
155.50
247
29.1
215.50
248
11.5
134.25
249
32.3
201.00
250
28.3
186.75
251
25.3
190.75
252
30.7
207.50
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