Question

In: Statistics and Probability

Part 1: Using Excel’s Randbetween(0,9) function, generate 200 samples of five random numbers between 0 and...

Part 1:

Using Excel’s Randbetween(0,9) function, generate 200 samples of five random numbers between 0 and 9, calculate the mean of each sample. Show me the list of the 200 means. Typically, they should look like: 4.8, 3.6, 4.4, 6.0, etc.

Part 2:

Using Excel, calculate the overall mean of the 200 sample means (the average of the averages). This should be around 4.5.

Part 3:   

Using Excel, calculate the standard error of the mean (SEM)  (i.e. the standard deviation of the 200 sample means). We established in the previous simulation that the population average is 4.5 and the standarddeviation of the population is 2.87.

Since the SEM=  σ= σ/√n. The SEM therefore is 1.28. Thus, the standard deviation of the 200 sample means should be approximately 1.28.

Part 4:

Using Excel, make the histogram of the 200 sample means (sampling distribution of the mean) (use interval size 1, i.e., 0-1, 1-2, 2-3, …8-9). According to the Central Limit Theorem a bell shaped curve should appear. Show me this graph.

Part 5:

Discuss the intuitive logic of the Central Limit Theorem. Discuss the implications of part 4 in this context.  (My videos might help here.)

Part 6:

Use 2 methods to find P (>6.3), (with n=5 as in Parts 1-4): First the z-method of chapter 7 and then by simply counting how many of your 200   were above 6.3.

  

Part 7:

Discuss the standard error of the mean.

Solutions

Expert Solution

Part-1

using Randbetween(0,9) this code in excel

                                                 

Sample

R1

R2

R3

R4

R5

Sample mean

standard deviation

SEM

1

8

7

1

0

3

3.8

3.564

1.594

2

9

2

2

0

6

3.8

3.633

1.625

3

4

3

6

9

0

4.4

3.362

1.503

4

7

3

5

2

8

5

2.550

1.140

5

4

6

1

5

2

3.6

2.074

0.927

6

2

8

7

5

9

6.2

2.775

1.241

7

9

3

8

2

9

6.2

3.421

1.530

8

8

1

4

8

9

6

3.391

1.517

9

5

9

8

0

0

4.4

4.278

1.913

10

3

8

4

1

5

4.2

2.588

1.158

11

1

0

1

5

5

2.4

2.408

1.077

12

1

9

9

7

1

5.4

4.099

1.833

13

8

1

7

6

1

4.6

3.362

1.503

14

0

8

6

0

0

2.8

3.899

1.744

15

3

3

9

6

1

4.4

3.130

1.400

16

1

2

8

8

8

5.4

3.578

1.600

17

8

7

3

3

9

6

2.828

1.265

18

5

3

2

0

6

3.2

2.387

1.068

19

5

8

0

0

5

3.6

3.507

1.568

20

4

3

2

5

8

4.4

2.302

1.030

21

4

5

7

0

1

3.4

2.881

1.288

22

2

7

6

4

9

5.6

2.702

1.208

23

6

0

5

1

8

4

3.391

1.517

24

8

3

5

3

7

5.2

2.280

1.020

25

2

1

1

2

4

2

1.225

0.548

26

5

7

1

7

3

4.6

2.608

1.166

27

8

5

8

7

3

6.2

2.168

0.970

28

7

2

7

3

4

4.6

2.302

1.030

29

3

3

8

2

5

4.2

2.387

1.068

30

8

7

6

2

1

4.8

3.114

1.393

31

6

9

0

5

9

5.8

3.701

1.655

32

4

5

8

8

3

5.6

2.302

1.030

33

2

2

9

6

3

4.4

3.050

1.364

34

8

5

2

3

6

4.8

2.387

1.068

35

6

2

7

7

5

5.4

2.074

0.927

36

4

9

7

1

9

6

3.464

1.549

37

2

6

1

3

3

3

1.871

0.837

38

9

3

1

2

3

3.6

3.130

1.400

39

6

8

5

2

0

4.2

3.194

1.428

40

8

7

2

2

9

5.6

3.362

1.503

41

1

5

7

8

1

4.4

3.286

1.470

42

8

7

4

7

9

7

1.871

0.837

43

0

3

1

6

2

2.4

2.302

1.030

44

7

3

9

4

2

5

2.915

1.304

45

4

9

7

2

1

4.6

3.362

1.503

46

5

8

4

0

6

4.6

2.966

1.327

47

6

9

6

0

3

4.8

3.421

1.530

48

4

7

1

3

4

3.8

2.168

0.970

49

4

6

5

9

5

5.8

1.924

0.860

50

8

1

1

5

9

4.8

3.768

1.685

51

3

3

7

4

3

4

1.732

0.775

52

9

9

7

9

4

7.6

2.191

0.980

53

8

9

4

6

7

6.8

1.924

0.860

54

7

0

0

6

2

3

3.317

1.483

55

1

1

6

1

2

2.2

2.168

0.970

56

5

4

0

3

6

3.6

2.302

1.030

57

4

7

5

9

0

5

3.391

1.517

58

8

3

2

2

1

3.2

2.775

1.241

59

6

2

9

6

4

5.4

2.608

1.166

60

9

4

7

8

1

5.8

3.271

1.463

61

7

6

6

3

5

5.4

1.517

0.678

62

2

4

9

2

6

4.6

2.966

1.327

63

6

5

0

1

3

3

2.550

1.140

64

6

5

5

1

4

4.2

1.924

0.860

65

6

6

3

9

6

6

2.121

0.949

66

5

5

6

4

3

4.6

1.140

0.510

67

9

7

9

4

5

6.8

2.280

1.020

68

1

2

0

9

2

2.8

3.564

1.594

69

7

3

7

6

8

6.2

1.924

0.860

70

5

9

9

7

8

7.6

1.673

0.748

71

2

6

3

4

3

3.6

1.517

0.678

72

1

2

2

8

2

3

2.828

1.265

73

9

4

0

3

1

3.4

3.507

1.568

74

4

3

0

5

7

3.8

2.588

1.158

75

8

0

8

4

7

5.4

3.435

1.536

76

8

6

9

4

8

7

2.000

0.894

77

5

3

9

3

7

5.4

2.608

1.166

78

5

1

9

6

4

5

2.915

1.304

79

4

6

3

4

4

4.2

1.095

0.490

80

5

9

0

2

7

4.6

3.647

1.631

81

8

0

4

6

9

5.4

3.578

1.600

82

3

5

5

3

0

3.2

2.049

0.917

83

4

8

6

5

2

5

2.236

1.000

84

8

9

4

8

0

5.8

3.768

1.685

85

1

9

2

2

0

2.8

3.564

1.594

86

1

3

1

5

4

2.8

1.789

0.800

87

8

3

4

7

7

5.8

2.168

0.970

88

8

1

2

4

5

4

2.739

1.225

89

7

6

9

2

5

5.8

2.588

1.158

90

5

1

2

5

8

4.2

2.775

1.241

91

8

1

4

3

2

3.6

2.702

1.208

92

9

9

1

5

8

6.4

3.435

1.536

93

5

8

7

9

1

6

3.162

1.414

94

3

3

2

9

2

3.8

2.950

1.319

95

1

9

6

8

1

5

3.808

1.703

96

4

7

5

2

3

4.2

1.924

0.860

97

7

8

1

4

2

4.4

3.050

1.364

98

9

6

3

6

4

5.6

2.302

1.030

99

9

4

3

6

6

5.6

2.302

1.030

100

8

4

6

6

7

6.2

1.483

0.663

101

0

0

3

5

3

2.2

2.168

0.970

102

2

0

2

0

9

2.6

3.715

1.661

103

7

0

8

0

0

3

4.123

1.844

104

6

5

2

7

5

5

1.871

0.837

105

7

4

4

7

9

6.2

2.168

0.970

106

1

6

8

3

1

3.8

3.114

1.393

107

4

8

3

6

6

5.4

1.949

0.872

108

4

8

0

7

5

4.8

3.114

1.393

109

8

9

8

8

0

6.6

3.715

1.661

110

8

0

8

5

5

5.2

3.271

1.463

111

6

3

0

3

7

3.8

2.775

1.241

112

3

2

8

5

7

5

2.550

1.140

113

3

8

0

4

0

3

3.317

1.483

114

2

8

8

8

9

7

2.828

1.265

115

4

6

7

2

0

3.8

2.864

1.281

116

3

5

3

1

8

4

2.646

1.183

117

8

2

2

3

4

3.8

2.490

1.114

118

4

8

1

3

2

3.6

2.702

1.208

119

7

8

4

9

7

7

1.871

0.837

120

3

2

1

7

2

3

2.345

1.049

121

6

6

6

1

5

4.8

2.168

0.970

122

5

0

9

7

4

5

3.391

1.517

123

8

0

8

4

8

5.6

3.578

1.600

124

6

8

8

9

5

7.2

1.643

0.735

125

4

6

3

3

1

3.4

1.817

0.812

126

7

3

6

7

0

4.6

3.050

1.364

127

6

9

8

3

9

7

2.550

1.140

128

7

6

1

4

9

5.4

3.050

1.364

129

7

0

3

7

6

4.6

3.050

1.364

130

6

9

5

5

3

5.6

2.191

0.980

131

4

4

3

9

8

5.6

2.702

1.208

132

8

3

2

8

3

4.8

2.950

1.319

133

0

3

4

3

0

2

1.871

0.837

134

5

1

0

7

9

4.4

3.847

1.720

135

5

4

3

9

9

6

2.828

1.265

136

4

2

4

6

7

4.6

1.949

0.872

137

4

5

3

0

9

4.2

3.271

1.463

138

5

0

0

1

3

1.8

2.168

0.970

139

7

1

1

1

1

2.2

2.683

1.200

140

8

9

8

9

1

7

3.391

1.517

141

8

3

0

1

0

2.4

3.362

1.503

142

4

7

7

5

5

5.6

1.342

0.600

143

8

3

6

6

4

5.4

1.949

0.872

144

1

9

1

9

2

4.4

4.219

1.887

145

5

2

9

1

2

3.8

3.271

1.463

146

1

3

8

5

8

5

3.082

1.378

147

8

1

6

1

4

4

3.082

1.378

148

6

0

9

9

4

5.6

3.782

1.691

149

8

7

9

0

2

5.2

3.962

1.772

150

5

3

0

6

5

3.8

2.387

1.068

151

6

9

4

9

9

7.4

2.302

1.030

152

3

2

2

1

5

2.6

1.517

0.678

153

9

1

1

0

2

2.6

3.647

1.631

154

9

0

9

7

0

5

4.637

2.074

155

4

1

4

5

3

3.4

1.517

0.678

156

5

3

0

0

8

3.2

3.421

1.530

157

1

0

0

4

4

1.8

2.049

0.917

158

6

1

5

9

2

4.6

3.209

1.435

159

0

4

9

4

7

4.8

3.421

1.530

160

4

5

5

6

6

5.2

0.837

0.374

161

8

8

8

3

2

5.8

3.033

1.356

162

3

7

9

0

0

3.8

4.087

1.828

163

1

1

5

7

9

4.6

3.578

1.600

164

0

7

6

0

5

3.6

3.362

1.503

165

8

2

4

3

6

4.6

2.408

1.077

166

0

5

9

4

1

3.8

3.564

1.594

167

6

1

0

3

1

2.2

2.387

1.068

168

5

5

4

2

6

4.4

1.517

0.678

169

6

1

5

7

6

5

2.345

1.049

170

8

8

3

3

1

4.6

3.209

1.435

171

6

4

5

8

3

5.2

1.924

0.860

172

1

0

8

3

5

3.4

3.209

1.435

173

4

5

1

7

2

3.8

2.387

1.068

174

8

5

5

5

0

4.6

2.881

1.288

175

9

9

3

9

3

6.6

3.286

1.470

176

5

6

5

7

1

4.8

2.280

1.020

177

3

4

7

1

9

4.8

3.194

1.428

178

8

3

8

4

3

5.2

2.588

1.158

179

3

1

5

5

7

4.2

2.280

1.020

180

8

6

5

3

9

6.2

2.387

1.068

181

8

0

4

1

3

3.2

3.114

1.393

182

3

6

6

8

8

6.2

2.049

0.917

183

5

1

1

9

9

5

4.000

1.789

184

3

6

6

2

7

4.8

2.168

0.970

185

0

7

8

6

4

5

3.162

1.414

186

3

2

4

6

5

4

1.581

0.707

187

4

6

3

6

6

5

1.414

0.632

188

8

6

8

0

3

5

3.464

1.549

189

7

5

5

7

0

4.8

2.864

1.281

190

9

4

3

8

6

6

2.550

1.140

191

3

6

3

8

2

4.4

2.510

1.122

192

2

5

0

0

6

2.6

2.793

1.249

193

6

4

1

8

9

5.6

3.209

1.435

194

1

8

6

3

2

4

2.915

1.304

195

6

9

4

2

7

5.6

2.702

1.208

196

7

6

8

9

2

6.4

2.702

1.208

197

5

3

6

6

6

5.2

1.304

0.583

198

3

7

8

8

5

6.2

2.168

0.970

199

4

4

2

6

8

4.8

2.280

1.020

200

5

3

7

2

2

3.8

2.168

0.970

Part 2

Overall mean

4.56

Part 3

200 sample mean standard deviation

2.732

Part-2

Using Avrage() code we calculate the sample mean of the each sample and the overall mean also calculated and we find that overall mean is arround 4.5.as shown in below

part-3

STDEV using this code we calculate the sample std. deviation for each sample and sample error mean also in below.

Overall mean = 4.56

200 sample mean standard deviation = 2.73

orchestra answered 2 years ago
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To generate 100 random numbers between 1-100 in a randomData.txt file To read the 100 random numbers from randomData.txt and store them in an array Print the data in the array Find the smallest and the largest of the random numbers and their array position Insert an element of value100 in the 51th position of the array Delete all the elements of the array having values between 50-80 and print the residual array Sort the data in the final array(residual)...
For this problem, you will write a program using two queues. Generate n random numbers between...
For this problem, you will write a program using two queues. Generate n random numbers between 10 and 100 (both inclusive), where n>9. The value of n should be taken as input from the user and n should be >9. The numbers could be duplicated. Enqueue all these numbers to the first queue. The objective is to find the numbers whose sum of digits is odd and enqueue them to the second queue. The remaining numbers (whose sum of digits...
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