GENERAL MATHS CALCULATION

QUESTION

SOLUTION

Climate Change Report

May 18

2012

We investigate the climatic changes over the past century with the data from 1900 to 2009. We have presented the graphs, statistical summary and the hypothesis testing to give a clear image of the climatic changes over the period. There have been significant changes in the climate over the period because of the global warming and the depleting forest cover.

A Hypothesis Testing Project

 


 

Table of Contents

A Hypothesis Testing Project0

Introduction. 2

Hypothesis. 2

Data Collection methods. 3

Methods. 3

Comparisons for the Climatic Changes. 3

The Statistical Summary. 8

Hypothesis Analysis with T-tests. 1

Hypothesis test for Kuwait1

Hypothesis test for Melbourne. 1

Conclusion. 1

References. 1

Appendix-I1

Appendix-II2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Introduction

 

This document is a scientific hypothesis report in order to investigate the “Climatic Changes” over past one decade. The climatic changes have been very fast since the development and the carbon emission rates have soaring high through out. The depleting forest cover and the exhausts from the automobiles and the industries have changed the temperature and the rainfall through out the world. The Icebergs are melting and the level of the sea water has been changing. (Rumsey,2009)There are a lot of climatic variations introduced as result of the global warming.

 Here in this report, we would not investigate the reasons and the impacts of global warming but the point of investigation is to analyze the changes in the temperature and the rainfall, from the data related to the same. We would use many statistical means to get to the conclusion.

Hypothesis  

 

As discussed above, there have been a lot of climatic changes through out the century. We would analyze the scenario by using the data for the two cities of Kuwait and Melbourne. We gathered the data from the climate change portal of World Bank. The portal can be reached as http://sdwebx.worldbank.org/climateportal. We have provided the tables of the data collected in Appendix-I for Kuwait and Appendix-II for Melbourne.

 Now, let us suppose the null hypothesis and the alternate hypothesis for the report as:

: There is no change in the temperature and the rainfall means have not changed in the past century.

: The means of the temperature and the rainfall changed in the past century.

 

 

 

 


We would calculate the means of the temperature and update the hypothesis as we proceed through the results.(Rumsey,2008)

Data Collection methods

 

Clearly, this is the secondary data available to us through a reliable and reputable source. Making primary data for the temperature and the rainfall would have been a time taking experience and the sample of the data collected would have lesser variations as compared to the large population of the whole century. So, we have collected the data from the historical part of the site. The data can be found out by clicking on a particular region.

Methods

 

We would now, discuss the various methods we are going to use for the project. The methods have been enlisted as follows:

       1. The column charts help us in the comparison of data along the identical horizontal axis.

      2. The line graphs show us the rise and fall of the data along the vertical axes in a more explicit way and let us compare the variables between the two graphs.

      3.  Descriptive statistics give the values of different statistical values related to the data.

      4. One sample t-tests compares the means of the sample with population and gives the reason whether to accept the null hypothesis. (Boslough,2011)

Comparisons for the Climatic Changes

 

We have made the column charts of the temperature (in degree Celsius) from the data available to us in the Appendix-I and Appendix-II. Similarly, we have made the line-chart of average rainfall of the two cities from January to December during the different periods which can be found from the chart titles above the graphs. It should be noted that we have taken two different vertical axes for each of the graphs shown here, the primary vertical axis for the temperature and the secondary vertical axis for the rainfall. However, we have only one horizontal corresponding to both the vertical axes, which gives the months of a year.(Buglear,2010)

We would now analyze the important deductions from the graphs shown here under. A look over the climate of Kuwait and Melbourne reveal the following pattern:

1.     The temperature patterns of the two cities show that the temperature of Kuwait increases from January to July and then, decreases from there to December, with December being the coldest month and July the hottest month, in general. Similarly, for Melbourne it can be said that the temperature decrease from January to the June-July period and then again increases towards December. The December and January are the hottest months while the mid-year months are comparatively colder.

2.     Another important difference can be pointed that the temperature extremes and the ranges are more in Kuwait than in Melbourne.

3.     The rainfall follows the temperature loosely in case of Melbourne than Kuwait.

4.     The rainfall is very less in Kuwait (0-20 mm) range while Melbourne receives fair amount of rainfall (0-100 mm) range.

The graphs of Kuwait in (Figure-4) and Melbourne in (Figure-8) for the period 1990-2006, show the change in the change in the patterns of the rainfall. There is little change in the rainfall in the starting months in Kuwait, but there is major change in the rainfall during September to December. In case of Melbourne there is a serious drop in the rainfall in the starting months, but in the last quarter the rainfall increases sharply. 

Figure 1: Kuwait Climate over 1900-1930 with temperatures represented by columns and rainfall by the line curves.

Figure 2: Kuwait Climate over 1930-1960 with temperatures represented by columns and rainfall by the line curves.

Figure 3: Kuwait Climate over 1960-1990 with temperatures represented by columns and rainfall by the line curves.

Figure 4: Kuwait Climate over 1960-2009 with temperatures represented by columns and rainfall by the line curves.

Figure 5: Melbourne Climate over 1900-1930 with temperatures represented by columns and rainfall by the line curves.

Figure 6: Melbourne Climate over 1930-1960 with temperatures represented by columns and rainfall by the line curves.

Figure 7: Melbourne Climate over 1960-1990 with temperatures represented by columns and rainfall by the line curves.

Figure 8: Melbourne Climate over 1990-2009 with temperatures represented by columns and rainfall by the line curves.

The Statistical Summary

 

Here, we present a statistical summary of the population of data shown in the two appendixes.


Temperature of Kuwait(1990-2009)

Mean

25.27333333

Standard Error

1.203830372

Median

25.1

Mode

35.4

Standard Deviation

8.340381473

Sample Variance

69.56196312

Kurtosis

-1.520623829

Skewness

-0.097598687

Range

24.9

Minimum

12.1

Maximum

37

Sum

1213.12

Count

48

 

Rainfall of Kuwait(1900-2009)

Mean

25.27333

Standard Error

1.20383

Median

25.1

Mode

35.4

Standard Deviation

8.340381

Sample Variance

69.56196

Kurtosis

-1.52062

Skewness

-0.0976

Range

24.9

Minimum

12.1

Maximum

37

Sum

1213.12

Count

48

 


 

 


Temperature of Melbourne

(1900-2009)

Mean

21.36042

Standard Error

0.724775

Median

21.9

Mode

21.4

Standard Deviation

5.02139

Sample Variance

25.21436

Kurtosis

-1.47678

Skewness

-0.20342

Range

15.2

Minimum

12.8

Maximum

28

Sum

1025.3

Count

48

Rainfall of Melbourne(1900-2009)

Mean

38.60208

Standard Error

3.808693

Median

28.3

Mode

21.5

Standard Deviation

26.3874

Sample Variance

696.2947

Kurtosis

3.030519

Skewness

1.723259

Range

121.2

Minimum

14.6

Maximum

135.8

Sum

1852.9

Count

48


Hypothesis Analysis with T-tests

Hypothesis test for Kuwait

Let us suppose the null hypothesis that there is no change in the mean of temperature, that is

 : There is no change in mean from 27 for temperature.

The T-value yields -0.072 for the samples 1990-2009, with the confidence level of 95% the T-value should be less than 3.106. Thus, we cannot reject the null hypothesis.

Hypothesis test for Melbourne

Let us suppose the null hypothesis that there is no change in the mean of temperature, that is

 : There is no change in mean from 21 degree Celsius for temperature.

 

The T-value yields -0.332 for the samples 1990-2009, with the confidence level of 95% the T-value should be less than 3.106. Thus, we cannot reject the null hypothesis.

Conclusion

There has been a lot of change in the climate since the past century but we do not have enough statistical evidence to reject the null hypothesis.

References

1. D. Rumsey  2009, Statistics for dummies

2. D. Rumsey  2008,Intermediate Statistics for dummies

3. Sharb Boslough and Andrew Watters 2011,Statistics in a nutshell .

4. John Buglear2010, Stats means Business ,

5. Data source , viewed on 18th may 2012,http://sdwebx.worldbank.org/climateportal

 

 

Appendix-I

 

The data for Kuwait has been presented in the following table. Statistical data include the temperature (in degrees) and the Rainfall (in mm).

 

 

 

 

Years

 

 

 

 

 

1900-1930

1930-1960

1960-1990

1990-2009

Months

Temperature

Rainfall

Temperature

Rainfall

Temperature

Rainfall

Temperature

Rainfall

Jan

15.1

14.8

15.5

14.8

17.5

7.2

13.7

16.7

Feb

20.3

14.9

19.6

13.8

18.4

12.9

19.2

7.9

Mar

20.9

15.3

25.1

16.3

24.5

6.3

24.5

14

Apr

30.7

4.7

30

5

30.7

3.9

30.8

3.1

May

34.2

0.5

33.7

0.5

34

0.5

35.4

0.5

Jun

36.2

0.8

34.9

0.5

35.4

0.8

37

0.5

Jul

35.4

0.6

35.7

0.5

34.9

0.6

36.6

0.6

Aug

33.4

0.5

33

0.5

32.4

0.5

33.5

0.5

Sep

27.4

1.9

27.22

2

25.1

1.9

27.5

1.9

Oct

20.3

12.8

20.8

8.6

20.7

9.2

20.7

17.6

Nov

15.7

17.8

14.5

16.4

14.7

12.9

14.6

3.3

Dec

12.9

16.9

13.9

13.9

12.8

12.8

12.1

43.6

 

Appendix-II

 

The data for Melbourne has been presented in the following table. Statistical data include the temperature (in degrees) and the Rainfall (in mm).

 

 

 

 

Years

 

 

 

 

 

1900-1930

1930-1960

1960-1990

1990-2009

Months

Temperature

Rainfall(mm)

Temperature

Rainfalll

Temperature

Rainfall

Temperature

Rainfall

Jan

27

93.6

27.4

79.7

26.5

93.9

26.4

40.6

Feb

24.5

89.9

25.3

47

25

56.3

26.3

63.7

Mar

21.4

29.8

21.4

18.5

21.4

27.8

21.9

43.4

Apr

18

22.5

17.9

27.4

15.8

38.1

18.8

35.3

May

14.1

24.1

15.2

30.4

14

16

14.6

21.9

Jun

12.8

21.3

14.9

24.5

14.2

30.1

14.8

26.4

Jul

15

27.1

15.8

22.4

14.5

16.3

15.5

21.5

Aug

19.5

18.4

18.8

14.6

18.2

22

18.9

15.8

Sep

21.9

21.5

22.1

29.6

22.4

16.2

22.8

17.6

Oct

26.7

16

25

28.8

23.9

31.3

26.5

15.4

Nov

28

24.2

26.1

57.8

26.4

57.6

27.8

44.7

Dec

27.4

67

26.9

79.5

27.6

49.6

28

135.8

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