Business Statistics Assignment



Business Statistics Assignment

Introduction

The purpose of this paper is to analyze the data set of fruits and vegetables market that supplies fresh produce to the supermarket outlets in NSW and Victoria, altogether there are seven variables that have been used for the rationale of this study. The list of these variables are provided below, in this paper we would be evaluating the customers in Sydney and Melbourne.

Column

Name

Description

A

ID Number

Customer Number

B

Customer

1= Coles

2= Private

3= Safeway

C

City

1= Sydney

2= Melbourne

D

Produce

1= Apple

2= Orange

3= Potato

4= Tomato

E

Quantity (sold/day)

Total quantity of produce sold per day

F

Price$/kg

Price in dollars per kilogram

G

% of produce damage

Percentage of produce damaged

A sample of 335 customers has been taken, that sell different fresh produce fruits and vegetable. The variable of price shows the price in dollars per kg sold by the customer in a particular city, whereas, the variable of damaged produced is also taken into consideration, additionally three of the variables (Customer, City, Produce) are taken in nominal scale, while the others are in scale measure. The random sample that has been generated through Excel is shown in the table below.

ID number

Customer

City

Produce

Quantity (sold/day)

Price $/kg

% of Produce Damage

80

1

2

3

529.41

0.36

7.92

42

1

2

2

11.10

2.99

1.13

68

1

1

3

321.88

1.25

5.25

327

3

2

4

360.72

1.53

8.41

218

3

1

1

177.78

2.31

4.07

211

2

2

4

85.31

2.34

4.58

74

1

2

3

396.38

0.81

7.07

63

1

1

3

337.18

1.04

5.88

3

1

1

1

235.31

1.88

5.36

186

2

1

4

478.02

1.90

7.30

307

3

1

4

461.12

1.09

9.73

120

2

2

1

305.48

2.05

4.85

17

1

2

1

140.02

2.72

3.04

145

2

2

2

344.16

0.94

7.18

104

2

1

1

182.03

2.28

4.16

313

3

1

4

82.03

2.05

5.62

261

3

2

2

83.06

2.29

3.23

329

3

2

4

118.80

2.29

4.76

127

2

2

1

162.50

2.50

3.70

157

2

1

3

318.86

1.29

5.13

154

2

1

3

396.85

1.57

4.79

165

2

2

3

342.91

1.38

5.36

132

2

1

2

135.82

2.76

1.82

229

3

1

1

104.44

2.58

3.46

272

3

2

2

331.46

1.12

6.64

227

3

1

1

111.50

2.51

3.67

30

1

1

2

346.85

1.57

5.29

194

2

1

4

5.00

2.28

4.79

286

3

1

3

344.85

0.93

6.21

183

2

1

4

381.38

1.42

8.74

160

2

1

3

356.88

0.75

6.75

140

2

2

2

35.82

2.76

1.82

197

2

1

4

16.03

2.62

3.57

33

1

1

2

323.28

1.85

4.45

182

2

1

4

461.12

1.65

8.05

318

3

1

4

42.45

2.45

4.18

86

1

1

4

95.95

2.88

2.63

112

2

1

1

69.82

2.91

2.47

190

2

1

4

18.00

2.82

2.85

54

1

2

2

275.88

1.82

4.54

116

2

2

1

350.09

1.53

6.41

178

2

2

3

502.84

0.73

6.81

87

1

1

4

9.00

2.96

2.34

20

1

2

1

188.77

2.23

4.51

133

2

1

2

72.61

3.33

0.11

136

2

1

2

364.28

1.35

5.95

222

3

1

1

154.48

2.47

3.59

303

3

2

3

523.45

0.45

7.65

128

2

2

1

145.21

2.67

3.19

320

3

2

4

404.24

1.59

8.23

Contingency tables are used to record and analyze the relationship between two or more variables, usually by nature qualitative (nominal or ordinal). The table allows us to see at a glance that the proportion of skilled men is approximately equal to the proportion of skilled women. However, both ratios are not identical and the statistical significance of the difference between them can be assessed with the ? ² test of Pearson, provided that the figures in the table are a random sample of a population. If the proportion of individuals in each column varies between the different rows and vice versa, we say that there is an association between two variables.

Customer * Produce Cross-tabulation

Count

Produce

Total

Apple

Orange

Potato

Tomato

Customer

Coles

3

4

4

2

13

Private

6

5

5

7

23

Safe-way

4

2

2

6

14

Total

13

11

11

15

50

The contingency table is a particular way of representing simultaneously two characters observed on the same population, if they are discrete or continuous and grouped into classes. The table above shows that most of the customers from Coles have produces potatoes, whereas only 2 tomatoes were produce by the Coles customer. On the other hand, it can be mentioned that Safeway customers have produce the tomatoes in higher quantity than any other fruit and vegetable. Overall, it can be noted that private customers are highest producers in the fruit and vegetable market.

Statistics

Produce

Price/KG

Percentage Of Produce Damage

N

Valid

50

50

50

Missing

285

285

285

Mean

2.56

1.9170

4.9848

Median

3.00

1.9750

4.7900

Std. Deviation

1.181

.75377

2.11331

Variance

1.394

.568

4.466

Report

Percentage Of Produce Damage

Customer

Mean

N

Std. Deviation

Coles

4.5700

13

1.90883

Private

4.7991

23

2.18408

Safe way

5.6750

14

2.15678

Total

4.9848

50

2.11331

ANOVA Table

Sum of Squares

df

Mean Square

F

Sig.

Percentage Of Produce Damage * Customer

Between Groups

(Combined)

9.699

2

4.849

1.090

.345

Within Groups

209.140

47

4.450

Total

218.839

49

In this section we will see how to test the null hypothesis from two means from two samples (or subgroups) independent. We will actually judge whether two means are equal in population-Based on the result of the comparison between these two samples. The technique used is called t-test for independent samples (Independent sample t test). This technique is used to compare two groups, created by a categorical variable, based on their average measurement (continuous variable).

Null hypothesis

There is no difference between the averages of two groups in the ...