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(solution) Question 3. (Statistical Inferences: Two Populations; 7 marks)


Question 3.   (Statistical Inferences: Two Populations; 7 marks)

Safe Driving:             Recent studies seem to indicate that using a mobile phone while driving is dangerous. One reason for this is that a driver?s reaction times may slow while he or she is talking on the phone. Researchers measured the reaction times of 180 drivers who owned a mobile phone, 100 drivers on the phone and 80 drivers not on the phone. The reaction times were recorded (in seconds). Can we conclude that the reaction times are slower for drivers using mobile phones? Test using a = 0.05.


Question 1 Annual returns (%)

 

Year 2014

 

Year 2015 7.72

 

5.33

 

11.80

 

6.14

 

6.05

 

6.62

 

8.01

 

9.34

 

6.75

 

10.93

 

5.22

 

8.26

 

6.32

 

7.35

 

9.01

 

5.73

 

7.39

 

6.59

 

7.51

 

7.37

 

3.34

 

6.13

 

7.46

 

6.78

 

4.12

 

6.87

 

5.93

 

6.58

 

5.94

 

5.95

 

5.11

 

7.10

 

5.92

 

5.62

 

7.92

 

5.85

 

5.04

 

6.80

 

7.97

 

5.15

 

7.96

 

9.60 5.99

 

3.73

 

6.15

 

3.24

 

4.73

 

5.74

 

7.68

 

8.53

 

5.81

 

7.58

 

3.95

 

8.10

 

7.21

 

2.63

 

6.66

 

5.14

 

3.82

 

5.26

 

1.82

 

6.82

 

2.11

 

3.22

 

6.75

 

4.75

 

2.50

 

6.26

 

4.12

 

7.07

 

4.39

 

5.12

 

3.74

 

6.93

 

5.03

 

4.93

 

6.39

 

4.63

 

3.74

 

6.75

 

5.27

 

4.51

 

6.26

 

7.99 Question 2

 

Orders ($) 63.46

 

53.51

 

96.67

 

113.00

 

72.52

 

53.88

 

77.86

 

99.31

 

59.26

 

65.64

 

110.15

 

46.28

 

105.15

 

108.35

 

77.82

 

51.28

 

79.15

 

104.93

 

46.31

 

89.44

 

56.92

 

90.41

 

85.28

 

84.36

 

92.91

 

75.43

 

90.37

 

83.58

 

76.08

 

70.42

 

77.74

 

107.17

 

86.32

 

84.78

 

66.14

 

103.91

 

83.55

 

76.55

 

83.98

 

64.93

 

92.23

 

119.83 Question 3

 

Reaction time on phone 0.747

 

0.536

 

0.834

 

0.671

 

1.031

 

0.605

 

0.936

 

0.648

 

0.590

 

1.231

 

0.928

 

1.148

 

0.702

 

0.479

 

1.013

 

0.509

 

1.093

 

0.793

 

0.662

 

0.691

 

0.559

 

0.904

 

0.576

 

0.756

 

0.995

 

0.555

 

0.933

 

0.790

 

0.772

 

0.625

 

0.780

 

0.946

 

0.589

 

1.026

 

0.893

 

0.714

 

0.742

 

0.683

 

0.923

 

0.545

 

0.574

 

0.593 6.50

 

7.00

 

8.23

 

6.56

 

5.16

 

7.61

 

6.07

 

7.63

 

6.83

 

4.39

 

5.54

 

6.75

 

4.91

 

6.62

 

6.57

 

5.36

 

6.01

 

7.27

 

4.00

 

7.64

 

5.84

 

6.83

 

5.39 5.38

 

4.76

 

7.74

 

4.26

 

5.98

 

5.62

 

3.17

 

4.81

 

5.92

 

3.07

 

5.91

 

5.27

 

0.90

 

5.31

 

4.28

 

3.40

 

4.74

 

6.71

 

3.02

 

6.90

 

4.72

 

5.12

 

3.07 96.87

 

82.13

 

92.45

 

78.23

 

61.99

 

89.75

 

70.62

 

82.49

 

65.89

 

41.98

 

77.33

 

103.62

 

86.41

 

51.95

 

94.88

 

82.89

 

116.51

 

69.31

 

66.37

 

105.40

 

99.75

 

76.79

 

80.56

 

88.99

 

117.94

 

52.84

 

75.37

 

56.45

 

80.69

 

82.13

 

92.45

 

78.23

 

61.99

 

89.75

 

70.62

 

82.49

 

65.89

 

41.98

 

77.33

 

103.62

 

101.07

 

87.59

 

100.09 0.821

 

0.740

 

0.720

 

0.794

 

0.554

 

0.606

 

0.661

 

0.514

 

0.831

 

0.832

 

0.535

 

0.814

 

0.971

 

0.789

 

0.622

 

0.844

 

0.776

 

0.666

 

0.787

 

0.893

 

0.710

 

0.939

 

0.868

 

0.945

 

0.677

 

0.831

 

0.860

 

0.746

 

0.524

 

0.832

 

0.676

 

1.022

 

0.609

 

0.933

 

0.646

 

0.591

 

1.229

 

0.863

 

0.629

 

0.830

 

0.732

 

0.703

 

0.693

 

0.836 0.916

 

1.011

 

0.859

 

0.838

 

0.614

 

0.851

 

0.773

 

0.666

 

0.784

 

0.895

 

0.712

 

0.942

 

0.872

 

0.779 Reaction time not on phone 0.573

 

0.652

 

0.891

 

0.723

 

0.962

 

0.551

 

0.717

 

0.803

 

0.812

 

0.937

 

0.974

 

0.733

 

0.718

 

0.451

 

0.898

 

0.965

 

0.577

 

0.593

 

0.946

 

0.599

 

0.990

 

0.699

 

0.709

 

0.608

 

0.842

 

0.970

 

0.528

 

0.483

 

0.755

 

0.706

 

0.484

 

0.982

 

0.912

 

0.682

 

0.798

 

0.539

 

0.634

 

0.578

 

0.779

 

0.691

 

0.837

 

0.560 Question 4

 

Person

 

Year 2014 ($) Year 2015 ($)

 

1

 

2

 

3

 

4

 

5

 

6

 

7

 

8

 

9

 

10

 

11

 

12

 

13

 

14

 

15

 

16

 

17

 

18

 

19

 

20

 

21

 

22

 

23

 

24

 

25

 

26

 

27

 

28

 

29

 

30

 

31

 

32

 

33

 

34

 

35

 

36

 

37

 

38

 

39

 

40

 

41

 

42 12870

 

12860

 

9991

 

12177

 

13133

 

12157

 

10895

 

12530

 

14689

 

9870

 

9971

 

7776

 

11613

 

11837

 

7508

 

7911

 

11941

 

11069

 

11998

 

12524

 

12162

 

32446

 

10218

 

10378

 

8040

 

7677

 

9984

 

10967

 

11472

 

9510

 

8789

 

10535

 

11875

 

10850

 

9368

 

10530

 

50178

 

10628

 

10649

 

7541

 

11787

 

7980 11609

 

13453

 

12102

 

10151

 

9508

 

9164

 

8030

 

9612

 

10179

 

7830

 

6933

 

6908

 

11131

 

6054

 

3932

 

6839

 

9246

 

11482

 

12914

 

6032

 

7689

 

28137

 

11230

 

11066

 

8011

 

9398

 

8745

 

5567

 

11178

 

8873

 

8983

 

9488

 

9691

 

8102

 

12884

 

10577

 

52691

 

8412

 

10299

 

8294

 

7826

 

7671 0.693

 

0.798

 

0.878

 

0.930

 

0.149

 

0.903

 

0.507

 

0.548

 

0.591

 

0.608

 

0.775

 

0.513

 

0.684

 

1.290

 

0.673

 

0.424

 

0.697

 

0.780

 

0.843

 

1.022

 

0.586

 

0.481

 

0.910

 

0.954

 

0.896

 

0.429

 

0.396

 

0.642

 

0.780

 

0.838

 

1.019

 

0.586

 

0.478

 

0.911

 

0.956

 

0.897

 

0.426

 

0.609 43

 

44

 

45

 

46

 

47

 

48

 

49

 

50

 

51

 

52

 

53

 

54

 

55

 

56

 

57

 

58

 

59

 

60

 

61

 

62

 

63

 

64

 

65

 

66

 

67

 

68

 

69

 

70

 

71

 

72

 

73

 

74

 

75

 

76

 

77

 

78

 

79

 

80

 

81

 

82

 

83

 

84

 

85

 

86 11351

 

8036

 

10932

 

11431

 

10227

 

8745

 

12129

 

11872

 

11268

 

12258

 

22517

 

12169

 

10397

 

11394

 

8300

 

10723

 

7858

 

9275

 

11622

 

9891

 

11322

 

8789

 

7452

 

7968

 

8562

 

7970

 

9241

 

12319

 

10865

 

7514

 

8927

 

10361

 

12172

 

7675

 

10232

 

12352

 

10668

 

8821

 

49028

 

12380

 

10061

 

11161

 

10120

 

8852 10254

 

10281

 

9733

 

4712

 

8551

 

6218

 

7616

 

12583

 

10686

 

8831

 

22753

 

8913

 

9836

 

7019

 

10950

 

12022

 

9810

 

10044

 

8058

 

9095

 

11297

 

7940

 

6859

 

13148

 

12232

 

13110

 

8058

 

13627

 

9986

 

7992

 

9481

 

11754

 

12262

 

9528

 

9704

 

10721

 

14836

 

10075

 

55846

 

7126

 

8783

 

7478

 

11948

 

9217 87

 

88

 

89

 

90

 

91

 

92

 

93

 

94

 

95

 

96

 

97

 

98

 

99

 

100

 

101

 

102

 

103

 

104

 

105

 

106

 

107

 

108

 

109

 

110

 

111

 

112

 

113

 

114

 

115 11103

 

9606

 

9466

 

12071

 

10005

 

9783

 

10228

 

11273

 

8652

 

10723

 

11341

 

7949

 

8849

 

31738

 

9719

 

8464

 

10476

 

8300

 

10190

 

11613

 

7853

 

11419

 

10920

 

12104

 

11426

 

11110

 

10113

 

11625

 

7760 9834

 

10363

 

13477

 

12109

 

11832

 

8034

 

14204

 

10447

 

11928

 

8875

 

9527

 

7742

 

6481

 

32844

 

13579

 

16237

 

8507

 

10775

 

12389

 

7090

 

9868

 

8519

 

9539

 

5659

 

6833

 

7415

 

5521

 

11085

 

9580

 


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