QUESTION

**Activity 8**

**Section 6: Signature Assignment**

The Signature Assignment for this course provides an opportunity for you to apply your skills and creativity to a self-designed fictitious study that employs statistical methodology with computational, analytical and interpretive skills. You will develop a fictitious problem and data set that utilizes specific statistics to analyze the data. The goal of this project is to allow you to demonstrate your cumulative knowledge, and to operationalize your learning in a scholarly manner.

The Signature Assignment and reflective essay should show how you:

(a) demonstrate mastery of the course material, and

(b) apply this knowledge to the real world.

**Required Reading:**

Review all course reading and resource as applicable

Reporting Statistics in APA Style website

Assignment 8 Paper – Fictitious Statistical Study

**Create and Analyze a Self-designed Fictitious Study**

For this activity you will undertake an analysis based on a self-designed fictitious study that utilizes statistical methodologies. You will first develop a fictitious problem to examine – it can be anything. For example, maybe you want to look at whether scores on a standardized college placement test (like the SAT) are related to the level of income a person makes 10 years after college; Or, whether those who participate in a Leadership Training program rated as better managers compared to those who do not; Or, whether ones political affiliation is related to gender. These are just a few examples; be creative and think about what piques your interest. You might also address a problem that you may want to look at in future research for a dissertation. You will use either EXCEL or SPSS to conduct the analysis.

Your analysis report should include the following components:

1. Describe your research study.

2. State a hypothesis.

3. List and explain the variables you would collect in this study. There must be a minimum of three variables and two must meet the assumptions for a correlational analysis.

4. Create a fictitious data set that you will analyze. The data should have a minimum of 30 cases, but not more than 50 cases.

5. Conduct a descriptive data analysis that includes the following:

a) a measure of central tendency

b) a measure of dispersion

c) at least one graph

6. Briefly interpret the descriptive data analysis.

7. Conduct the appropriate statistical test that will answer your hypothesis. It must be a statistical test covered in this course such as regression analysis, single t-test, independent t-test, cross-tabulations, Chi-square, or One-Way ANOVA. Explain your justification for using the test based on the type of data and the level of measurement that the data lends to for the statistical analysis.

8. Report and interpret your findings. Use APA style and include a statement about whether you reject or fail to reject the null hypothesis.

9. Copy and paste your Excel or SPSS data output and place it in an appendix.

Remember, the goal of this project is to show what you have learned in the course. Therefore, this project becomes a cumulative learning project where you can demonstrate what you have learned through all the previous assignments, readings and video presentations that you have watched.

Length: 10-14 pages (app. 350 words per page)

Your paper should demonstrate thoughtful consideration of the ideas and concepts that are presented in the course and provide new thoughts and insights relating directly to this topic. Your response should reflect scholarly writing and current APA standards. Be sure to adhere to Northcentral University’s Academic Integrity Policy

SOLUTION

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:

We would calculate the means of the temperature and update the hypothesis as we proceed through the results.

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.(Rumsey,2010)

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.

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(Boslough and Waters 2008). However, we have only one horizontal corresponding to both the vertical axes, which gives the months of a year.

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.

Regression Analysis between Temperature and Rainfall

Let us see the relationship between the temperature and the rainfall of Kuwait and Melbourne, one by one. We would analyze this section with the help of the scatter plots and the linear regression model. (Buglear,2008)

This is widely believed that the high temperatures are responsible for the higher rainfall. However, there may be variants in the thought because of the geography and other factors. The Rainfall plot of Kuwait shows that there is no relation-ship between the temperature and the rainfall as such there. This is confirmed by the value of the coefficient which is 0.623707. Thus the rainfall of Kuwait is affected by the reasons other than temperature.

Similarly, we plotted the rainfall of Melbourne with the temperature of the place. The plot shows us that the rainfall has a positive slope with temperature. However, when we look at the statistics of the regression analysis, the value of Coefficient of determination is still lower in this case (0.34512). Thus, in both the cases we have no relation ship between the temperature and the rainfall.

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.789751

R Square 0.623707

Adjusted R Square 0.615526

Standard Error 5.165853

Observations 48

ANOVA

df SS MS F Significance F

Regression 1 2034.679 2034.679 76.24506 2.53E-11

Residual 46 1227.558 26.68604

Total 47 3262.237

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept 27.72939 2.401995 11.54432 3.48E-15 22.89443 32.56436 22.89443 32.56436

X Variable 1 -0.78888 0.090346 -8.73184 2.53E-11 -0.97074 -0.60703 -0.97074 -0.60703

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.587469

R Square 0.34512

Adjusted R Square 0.330884

Standard Error 21.58477

Observations 48

ANOVA

df SS MS F Significance F

Regression 1 11294.35 11294.35 24.2419 1.14E-05

Residual 46 21431.5 465.9021

Total 47 32725.85

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%

Intercept -27.3407 13.75078 -1.9883 0.052747 -55.0196 0.338153 -55.0196 0.338153

X Variable 1 3.08715 0.62701 4.923606 1.14E-05 1.825045 4.349256 1.825045 4.349256

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. Rumsey D 2009., Statistics for dummies.

2. Rumsey D 2010., Intermediate Statistics for dummies.

3. Sharb Boslough and Andrew Watters 2008, Statistics in a nutshell

4. John Buglear 2008, Stats means Business

5. Data source , viewed on 22nd may 2012, http://sdwebx.worldbank.org/climateportal

6. “Statistics in excel”, viewed on 22nd may 2012, from http://www.ehow.com

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

JG43

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