Part I: Statistical Measures and Part II: Hypothesis Testing

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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    Part I: Statistical Measures and Part II: Hypothesis Testing

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    • 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 …

    • 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 …

    • You are hired as a statistical analyst for Silver’s Gym, and your boss wants to examine the relationship between body fat and weight in men who attend the gym. After compiling the data for …

    • 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 …