Information Management - Assignment 1

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Information Management: BBM500Assignment Part 1 Quantitative Methods

Student ID: 0963236 Page 1

For attention of

Professor Phillip Samouel

Information Management: BBM500

Assignment Part 1: Quantitative Methods

HS Gas Ltd: Average weekly production values generated on a Gas Mains Rehabilitation

Contract by Main Layers, Service Layers and Multi-Skilled teams.

Date: 31 March 2010

Word Count: 1,945

Student: ID 0963236


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Contents Page

Executive Summary Page 3

Research Criteria and Data Introduction Page 4

Question 1: Summary of the Characteristics of the Data Page 5

Question 2a: i) The assessment of a single sample mean average weekly turnover compared to the

population mean average weekly turnove r for the Gas Utility Contracts Page 8

Question 2a: ii) The Comparison of two independent population sample means namely average weekly

turnover of Main Laying Service teams and Multi -Skilled teams. Page 9

Question 2a: iii) The Comparison of Multiple Independent Sample Means to check Significant

differences in the Population Page 11

Appendices

Bibliography Page 22


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Executive Summary

HS Gas Ltd is an established, professional, utilities and civil engineering contracting company.

Re-branded in 2006 as HS Group Ltd to reflect its development into a multi-disciplinary contractor, it now embodies five specialised

operating Divisions, working together to provide clients with a complete, integrated contract solution. HS Gas Ltd is one of those

divisions and falls under the parent company of HS Group Ltd.

The Gas Utilities Division has just over 200 two man teams working on various contracts across the South of England. These

teams in turn are categorized into three different types namely Main Layers, Service Layers and Multi-Skilled teams. All three have

similar characteristics and skill levels but work on different parts of the installation and rehabilitation of gas mains.

I have taken these three skill set categories as independent populations within the total HS Gas Ltd team labour resources .

I can therefore conclude within a 95% significant degree of confidence by using statistical analysis the following:

Report

AVERAGE

SKILL Mean N Std. Deviation

1 4616.3645 33 1908.17953

2 1881.0861 18 581.62474

3 3711.3215 72 1759.25182

Total 3686.2986 123 1875.77175


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Research Criteria and Data Introduction

The objective of this research is to enforce the hypothesis that the Main Laying Teams (Skill Set 1) produce a higher average

weekly turnover than the Multi-Skilled Teams (Skill Set 3) and in turn is greater than the Service Laying Teams (Skill Set 2).

The three Skill Set categories are as follows within the Gas Industry:

Skill Set 1: Main Laying TeamsThey are responsible for laying gas mains (size range from 63mm to 600mm) within the existing and proposed new gas utilities

network.

Skill Set 2: Service Laying Teams

They are responsible for connecting the newly laid gas main up to residential and commercial properties which feed off the gas

network.

Skill Set 3: Multi-Skilled TeamsAs the title states they are skilled in both of the first two sets but are more used on smaller projects where it is not suitable to have

too many teams working i.e. small villages.

Raw data was taken from an in-house Database known to HS Gas as CAS9. Of the total 210 teams working on the HS Gas Ltd

contracts an amount of 129 were taken as observations. From the 129 teams 6 have been removed as outliers. The breakdown of

the sample for the remaining 123 is as shown in the Executive Summary.


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Question 1. Summary of the Characteristics of the Data

The average weekly value generated by HS Gas Ltd Teams using a workforce sample representative

of the Company as a whole.

By using Descriptive Statistics the following tables have been generated with the use of an initial sample of 129 teams (Skill Set 1,

2 and 3 See Appendices)

Descriptives

Statistic Std. Error

AVERAGE Mean 4034.6721 213.39820

95% Confidence Interval for Mean Lower Bound 3612.4273

Upper Bound 4456.9169

5% Trimmed Mean 3796.7776

Median 3421.1000

Variance 5874504.334

Std. Deviation 2423.73768

Minimum 1269.02

Maximum 11913.97

Range 10644.95

Interquartile Range 2991.72

Skewness 1.363 .213

Kurtosis 1.783 .423

Extreme Values

Case Number Value

AVERAGE Highest 1 111 11913.97

2 68 11680.36

3 25 11451.33

4 88 10882.76

5 45 10669.38

Lowest 1 43 1269.02

2 30 1294.09

3 86 1294.40

4 11 1318.45

5 73 1319.97


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OutliersWith a minimum of 1,269.02 and a maximum of 11,913.97 the range of 10,644.95 is high in comparison. Based on experience of

what teams can produce on a weekly basis one can assume that the extreme average values generated are unrealistic and

therefore these outliers should be removed from the analysis and not included.The skewness of the data is shown to be 1.363 which is slightly out of the acceptable range so that a normal distribution can occur.

The characteristics of a normal distribution have been achieved by removing six outliers. This was done by firstly removing the

highest values which were distorting the characteristics of a normal distribution.

The mean of 3,683.30 is comparative to the median of 3,314.49 which shows that the data is now more accurately representative

of what the weekly average teams values for Gas Utility teams should be.

The acceptable range of +/-1 for skewness has been achieved of 0.855. This shows that the data used is slightly positively skewed

but lies within the acceptable parameters.

The acceptable range of +/-2 for kurtosis has also been achieved of 0.370. This distribution curve is therefore slightly platykurtic.


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Descriptives


AVERAGE Mean 3686.2986 169.13264

95% Confidence Interval for Mean Lower Bound 3351.4837



Median 3314.4900



Minimum 1269.02

Maximum 9312.99

Range 8043.97


Skewness .855 .218

Kurtosis .370 .433

Extreme Values

Case Number Value


2 65 9130.38

3 22 8951.36

4 87 8171.21

5 44 8010.99

Lowest 1 43 1269.02

2 30 1294.09

3 86 1294.40

4 11 1318.45

5 73 1319.97

Data ObservationsI can be 95% confident that the average weekly turnover will be between 4,021.11 and 3,351.48.After comparing against

retrospective values generated on previous contracts I can accept that this is in line with regards to Main Laying, Service Laying

and Multi-Skilled teams within the Gas Utilities industry.

The sample mean is 3,683.30. The range was initially 10,644.95 which have now been reduced to 8,043.97.


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Normal distribution curve achieved after the relevant outliers were taken out

Question 2a: i) The assessment of a single sample mean average weekly turnover compared to thepopulation mean average weekly turnover for the Gas Utility Contracts. The average weekly turnover for teams within the Gas Utility Contracts can be taken to be 3,125. This figure has been deduced

from previous experience working on Gas Utility Contracts across the South West of England over the past 10 years by my

Commercial Director, Mr Dave Arnold of HS Gas Ltd. This is the figure used by him to complete any monthly f orecasting.

Therefore the sample mean of the teams must be compared to the population mean in order to assess the validity of the claim that

the figure used to complete forecasts and actual weekly turnover is accurate with a degree of confidence.

It is assumed that the population distribution is normal.

The Hypothesis Test:

- Null Hypothesis

HO: = 3,125 (Teams average weekly turnover South West of England)

- Alternative Hypothesis

HA: > 3,125 (The average weekly turnover for teams in South of England is greater than 3,125)

The sample mean of 3,686.29 is known to be higher than this and therefore the one tailed test is applied.


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- Level of Significance

= 0.05 Margin of Error is used

- Determination of the Appropriate Statistical Test

The Z test requires the standard deviation for the population which is not available and therefore the t test will be used.

The t test is more accurate because it considers the sample size. If the sample size increases there is no difference

between the Z and t test. (Kingston University Module: Information Management 11.9)

- Determination of the Critical Value

SPSS will be used to calculate this.

- Calculating the Test Statistic

SPSS will be used to calculate this

- Conclusion (SPSS Output)

One-Sample Statistics

N Mean Std. Deviation Std. Error Mean

AVERAGE 123 3686.2986 1875.77175 169.13264

One-Sample Test

Test Value = 3125

t df Sig. (2-tailed) Mean Difference

95% Confidence Interval ofthe

Difference

Lower Upper

AVERAGE 3.319 122 .001 561.29862 226.4837 896.1136

After completing the t test using the SPSS Statistical package, the p - value is shown to be 0.001

The p - value represents the exact probability that data as extreme as the data we have obtained would occur if the null hypothesis

is true. (Kingston University: Information Management 11.13)

The p value is divided by two due to the fact that the t distribution is symmetrical. Therefore the one-tailed p value is 0.0005.

The one-tailed p value of 0.0005 is less than the significance level of 0.05 and therefore we reject the HO

It can therefore be concluded with a 5% significance level that the sample mean is significantly greater than the population mean.


turnover of Main Laying Service teams and Multi-Skilled teams.Assumptions to be made of the following: The samples are Independent as they are based on different skill sets to complete work

on the gas contracts. The populations follow a normal distribution.


- Null Hypothesis

HO: Average Main Laying teams = Average Multi Skilled teams


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HA: Average Main Laying teams Average Multi Skilled teams

The two-tailed test is used to check whether there is any significant difference between them.




A t test of independent populations will be used. The Levenes test will provide information about the variances of the

two populations and the related hypothesis. The Null Hypothesis to be tested at = 0.05 as follows:

HO: 2Average Main Laying teams = 2Average Multi-Skilled teams

HA: The variances of the two populations are not equal

(Kingston University: Information Management 11.18)




SPSS will be used to calculate this. We have retained HO of equality of variances and therefore shall see the test statistic

of 2.383 (Kingston University: Information Management 11.19)


Group Statistics

SKILL N Mean Std. Deviation Std. Error Mean

AVERAGE 1 33 4616.3645 1908.17953 332.17142

3 72 3711.3215 1759.25182 207.32981

Independent Samples Test

Levene's Test

for Equality of

Variances t-test for Equality of Means

F Sig. t df

Sig. (2-

tailed)

Mean

Difference

Std. Error

Difference

95% Confidence Interval of

the Difference

Lower Upper

AVERAGE Equal

variances

assumed

.015 .903 2.383 103 .019 9.05043E2 3.79831E2 1.51738E2 1.65835E3

Equal

variances not

assumed

2.311 57.834 .024 9.05043E2 3.91565E2 1.21192E2 1.68889E3


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The SPSS output data shows that sample mean for Main Laying teams (Skill set 1) is 905.04 higher than that of the sample mean

for Multi-Skilled teams (Skill set 3).

The 2-tail sig of 0.019 is smaller than the (0.05) and therefore we reject HO and conclude that at a 5% level of significance there

is evidence of significant difference in the mean of the average weekly turnover of Main Laying and Multi -Skilled teams.

Question 2a: iii) The Comparison of Multiple Ind ependent Sample Means to check Significant

differences in the Population

Assumptions to be made of the following: 1) Data was obtained independently and randomly from the populations. 2) The

population follows a normal distribution. 3) The populations from which the data has been obtained have a common variance


- Null Hypothesis

HO: Average Main Laying teams = Average Service Laying teams = Average Multi-Skilled teams


HA: Not all s are the same or at least two s are not equal




There are more than two means and therefore ANOVA is employed. Levenes test for the assumption of Equality of

Variance will be employed. The Null Hypothesis to be tested at = 0.05 as follows:

HO: 2Average Main Laying teams = 2Average Service Laying teams = 2Average Multi-Skilled teams

Alternative hypothesis will be:

HA: Not all variances are the same or at least two variances are not equal






Report

AVERAGE


1 4616.3645 33 1908.17953

2 1881.0861 18 581.62474

3 3711.3215 72 1759.25182

Total 3686.2986 123 1875.77175


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Appendices

SPSS Raw Data:

IDMAINLAYER / SERVICELAYER / MULTISKILLED

TOTAL VALUEGENERATED

No OF WEEKSAVERAGE PER

WEEK

1 3 86,393.08 11 7,853.92

2 3 387,026.36 37 10,460.17

3 1 224,144.23 43 5,212.664 2 7,760.87 4 1,940.22

5 2 79,855.60 54 1,478.81

6 1 46,572.53 8 5,821.57

7 1 97,997.10 33 2,969.61

8 1 21,695.50 14 1,549.68

9 3 82,227.56 39 2,108.40

10 3 105,851.00 18 5,880.61

11 3 61,967.04 47 1,318.45

12 2 25,622.08 11 2,329.28

13 1 160,069.82 37 4,326.21

14 3 46,807.08 20 2,340.35

15 1 139,102.63 34 4,091.25

16 3 194,633.08 36 5,406.47

17 3 213,298.66 62 3,440.30

18 1 12,538.12 4 3,134.53

19 3 82,895.91 24 3,454.00

20 3 157,051.78 59 2,661.89

21 3 210,880.14 51 4,134.90

22 1 187,978.50 21 8,951.36

23 3 40,248.28 12 3,354.02

24 1 93,841.92 19 4,939.05

25 1 423,699.27 37 11,451.33

26 3 121,254.17 50 2,425.08

27 3 72,550.48 13 5,580.81

28 2 13,761.76 5 2,752.3529 1 164,406.56 48 3,425.14

30 2 3,882.26 3 1,294.09

31 3 64,190.38 48 1,337.30

32 3 70,003.15 13 5,384.86

33 3 171,030.98 60 2,850.52

34 3 25,995.97 8 3,249.50

35 3 77,649.48 15 5,176.63

36 3 113,959.50 48 2,374.16

37 1 187,486.64 35 5,356.76

38 3 76,489.05 53 1,443.19

39 3 156,009.50 59 2,644.23

40 3 61,552.79 16 3,847.05

41 3 299,232.21 46 6,505.0542 3 132,189.76 52 2,542.11

43 2 27,918.48 22 1,269.02

44 3 88,120.94 11 8,010.99

45 3 394,766.89 37 10,669.38

46 1 228,627.11 43 5,316.91

47 2 7,916.09 4 1,979.02

48 2 81,452.71 54 1,508.38

49 1 47,503.98 8 5,938.00


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50 1 99,957.04 33 3,029.00

51 1 22,129.41 14 1,580.67

52 3 83,872.11 39 2,150.57

53 3 107,968.02 18 5,998.22

54 3 63,206.38 47 1,344.82

55 2 26,134.52 11 2,375.87

56 1 163,271.21 37 4,412.74

57 3 47,743.22 20 2,387.16

58 1 141,884.68 34 4,173.08

59 3 198,525.74 36 5,514.6060 3 217,564.63 62 3,509.11

61 1 12,788.88 4 3,197.22

62 3 84,553.83 24 3,523.08

63 3 160,192.81 59 2,715.13

64 3 215,097.74 51 4,217.60

65 1 191,738.07 21 9,130.38

66 3 41,053.25 12 3,421.10

67 1 95,718.76 19 5,037.83

68 1 432,173.26 37 11,680.36

69 3 123,679.25 50 2,473.59

70 3 74,001.49 13 5,692.42

71 2 14,037.00 5 2,807.40

72 1 167,694.69 48 3,493.64

73 2 3,959.91 3 1,319.97

74 3 65,474.18 48 1,364.05

75 3 71,403.21 13 5,492.55

76 3 174,451.60 60 2,907.53

77 3 26,515.89 8 3,314.49

78 3 79,202.47 15 5,280.16

79 3 116,238.69 48 2,421.64

80 1 191,236.37 35 5,463.90

81 3 78,018.83 53 1,472.05

82 3 159,129.69 59 2,697.11

83 3 62,783.85 16 3,923.99

84 3 305,216.85 46 6,635.1585 3 134,833.56 52 2,592.95

86 2 28,476.85 22 1,294.40

87 3 89,883.36 11 8,171.21

88 3 402,662.22 37 10,882.76

89 1 233,199.65 43 5,423.25

90 2 8,074.41 4 2,018.60

91 2 83,081.77 54 1,538.55

92 1 48,454.06 8 6,056.76

93 1 101,956.18 33 3,089.58

94 1 22,572.00 14 1,612.29

95 3 85,549.56 39 2,193.58

96 3 110,127.38 18 6,118.19

97 3 64,470.51 47 1,371.7198 2 26,657.21 11 2,423.38

99 1 166,536.64 37 4,500.99

100 3 48,698.09 20 2,434.90

101 1 144,722.38 34 4,256.54

102 3 202,496.26 36 5,624.90

103 3 221,915.93 62 3,579.29

104 1 13,044.66 4 3,261.17

105 3 86,244.90 24 3,593.54


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106 3 163,396.67 59 2,769.44

107 3 219,399.70 51 4,301.95

108 1 195,572.83 21 9,312.99

109 3 41,874.31 12 3,489.53

110 1 97,633.13 19 5,138.59

111 1 440,816.72 37 11,913.97

112 3 126,152.84 50 2,523.06

113 3 75,481.52 13 5,806.27

114 2 14,317.74 5 2,863.55

115 1 171,048.58 48 3,563.51116 2 4,039.10 3 1,346.37

117 3 66,783.67 48 1,391.33

118 3 72,831.27 13 5,602.41

119 3 177,940.63 60 2,965.68

120 3 27,046.21 8 3,380.78

121 3 80,786.52 15 5,385.77

122 3 118,563.46 48 2,470.07

123 1 195,061.10 35 5,573.17

124 3 79,579.21 53 1,501.49

125 3 162,312.28 59 2,751.06

126 3 64,039.52 16 4,002.47

127 3 311,321.19 46 6,767.85

128 3 137,530.23 52 2,644.81

129 2 29,046.39 22 1,320.29

1: Main Layer Team (Total 36)

2: Service Layer Team (Total 18)

3: Multi-Skilled Team (Total 75)


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Question 1: Summary of the Characteristics of the Data

Descriptives


AVERAGE Mean 3740.9266 176.43323

95% Confidence Interval for

Mean

Lower Bound 3391.6879



Median 3334.2550



Minimum 1269.02

Maximum 10460.17

Range 9191.15


Skewness .992 .217

Kurtosis .851 .431

Extreme Values

Case Number Value


2 108 9312.99

3 65 9130.38

4 22 8951.36

5 87 8171.21

Lowest 1 43 1269.02

2 30 1294.09

3 86 1294.40

4 11 1318.45

5 73 1319.97


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Cases

Valid Missing Total

N Percent N Percent N Percent

AVERAGE 123 95.3% 6 4.7% 129 100.0%

Descriptives


AVERAGE Mean 3686.2986 169.13264

95% Confidence Interval for

Mean

Lower Bound 3351.4837



Median 3314.4900



Minimum 1269.02

Maximum 9312.99

Range 8043.97


Skewness .855 .218

Kurtosis .370 .433

Extreme Values

Case Number Value


2 65 9130.38

3 22 8951.36

4 87 8171.21

5 44 8010.99

Lowest 1 43 1269.02

2 30 1294.09

3 86 1294.40

4 11 1318.45

5 73 1319.97


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Question 2a: i) The assessment of a single sample mean average weekly turnover compared to the

population mean average weekly turnover for the Gas Utility Contracts

One-Sample Statistics

N Mean Std. Deviation Std. Error Mean

AVERAGE 123 3686.2986 1875.77175 169.13264

One-Sample Test

Test Value = 3125

t df Sig. (2-tailed) Mean Difference

95% Confidence Interval ofthe

Difference

Lower Upper

AVERAGE 3.319 122 .001 561.29862 226.4837 896.1136


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turnover of Main Laying Service teams and Multi-Skilled teams.Group Statistics

SKILL N Mean Std. Deviation Std. Error Mean

AVERAGE 1 33 4616.3645 1908.17953 332.17142

3 72 3711.3215 1759.25182 207.32981

Independent Samples Test

Levene's Test

for Equality of

Variances t-test for Equality of Means

F Sig. t df

Sig. (2-

tailed)

Mean

Difference

Std. Error

Difference

95% Confidence Interval of

the Difference

Lower Upper

AVERAGE Equal

variancesassumed

.015 .903 2.383 103 .019 9.05043E2 3.79831E2 1.51738E2 1.65835E3

Equal

variances not

assumed

2.311 57.834 .024 9.05043E2 3.91565E2 1.21192E2 1.68889E3

Question 2a: iii) The Comparison of Multiple Independent Sample Means to check Significant

differences in the Population Report

AVERAGE


1 4616.3645 33 1908.17953

2 1881.0861 18 581.62474

3 3711.3215 72 1759.25182

Total 3686.2986 123 1875.77175

ANOVA

AVERAGE

Sum ofSquares df Mean Square F Sig.

Between Groups 87249088.794 2 43624544.397 15.306 .000

Within Groups 342010310.346 120 2850085.920

Total 429259399.140 122

Multiple Comparisons


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AVERAGE

Tukey HSD

(I)SKILL (J)SKILL Mean Difference (I-J) Std. Error Sig.

95% Confidence Interval

Lower Bound Upper Bound

1 2 2735.27843*

494.67600 .000 1561.3390 3909.2179

3 905.04302* 354.89543 .032 62.8236 1747.2625

2 1 -2735.27843*

494.67600 .000 -3909.2179 -1561.3390

3 -1830.23542*

444.88497 .000 -2886.0134 -774.4575

3 1 -905.04302* 354.89543 .032 -1747.2625 -62.8236

2 1830.23542*

444.88497 .000 774.4575 2886.0134

*. The mean difference is significant atthe 0.05 level.


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Bibliography

All data has been extrapolated from CAS9 (in-house database) at HS Gas Ltd. (forms part of HS Group Ltd). The data represents

works completed by the various gangs over a period of roughly 3 years.

1. Mr Dave Arnold Director, HS Gas Ltd, March 2010

2. Kingston University, Information Management, 2008

3. Statistics for Dummies, by Deborah Rumsey, Ph.D., Wiley Publishing Inc., 2003

Information Management - Assignment 1

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