## (solution) Question 2. (Statistical Inferences: Single Population; 2 + 6 = 8

Question 2.   (Statistical Inferences: Single Population; 2 + 6 = 8 marks)

Feasibility Study:      Companies that sell groceries over the Internet are called e-grocers. Customers enter their orders, pay by credit card and receive delivery by truck. To determine whether an e-grocery would be profitable in one large city, a potential e-grocer offered the service and recorded the size of the order for a random sample of 85 customers. The data are stored in the data file.

Estimate with 95% confidence the average order in the city.

Financial analysis indicates that to be profitable the average order would have to be more than \$80. Can we infer from the data that an e-grocery will be profitable in the city? Test using a = 0.05.

Due in two hours !!!!!!!!!!!!!!!

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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