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This assignment provides students with opportunity to:

Combine statistical analysis and report writing skills to prepare a concise, non-technical business report,

Draw a random sample to complete statistical analysis,

Develop and enhance computing skills, specifically the use of the built-in functions in MS Excel and MS Word

Apply statistical techniques to a data set, and

Reinforce taught concepts including descriptive statistics, sampling and estimation, hypothesis testing, correlation and regression.

## Data Source and Sections

Margaret the CEO of a Human Capital Management company in Melbourne recently attended a TED Talk in which Michael Green discussed the importance of the 2030 United Nation Sustainable Development Goals. Michael presented challenges that countries around the world would face to meet the UN Sustainable Development Goals and elaborated on the importance of the Social Progress Index in that process. Some of the questions tackled include; what are the UN Sustainable Development Goals? And how we can make the world a better place by 2030? After the seminar, Margaret decided to further study the importance of the Social Progress Index and compare countries based on their performance at each sub category of this index. This study therefore sought to answer the CEO’s concerns in relation to the Social Progress Index.

Data for this study refers to the 2017 Social Progress Index data set and it contains about 182 countries. The sections of the report include statistical analysis (descriptive statistics, confidence intervals, correlation and regression) conclusion and limitations.

Most of the countries included in the study were countries in Africa (52%, n = 46). American continent was represented by 26% (n = 23) while Asia had a 22% (n = 19) representation.

The average percent of people with access to improved  sanitation facilities was found to be 58.73% with some countries having a 100% access to improved sanitation facilities and the country with the lowest rate recording a mere 10.88% access to improved sanitation facilities. On average, 21.99% of traffic deaths was recorded in the selected countries with some countries recording as high as 73.4% while others recording as low as 3.60%. In terms of press freedom index, an average index of 36.38% was recorded with the country with highest index score scoring 83.92% and the lowest score being 11.10%.

The selected countries emitted an average of 725.93 greenhouse emissions with some countries emitting as high as 11031.69 while others emitting as low as 168.22.

Average corruption index stood at 36.45% with the highest index being 82% and the lowest index being 14%. Women’s average years in school for the selected sample was found to be 8.12, however, some countries had an average of 15.68 while others had an average of 0.98.

 Access to improved sanitation facilities Traffic deaths Press Freedom Index Greenhouse gas emissions Corruption Women's average years in school Mean 58.73 21.99 36.38 725.93 36.45 8.12 Standard Error 3.23 0.99 1.60 124.78 1.56 0.41 Median 61.24 23.50 31.99 523.15 34.00 8.65 Mode 100.00 24.10 57.89 #N/A 26.00 #N/A Standard Deviation 30.32 9.26 14.98 1170.52 14.65 3.88 Sample Variance 919.57 85.73 224.26 1370115.07 214.69 15.05 Kurtosis -1.49 9.70 1.20 70.98 0.78 -0.93 Skewness -0.13 1.69 1.07 8.06 0.99 0.07 Range 89.12 69.80 72.82 10863.47 68.00 14.70 Minimum 10.88 3.60 11.10 168.22 14.00 0.98 Maximum 100.00 73.40 83.92 11031.69 82.00 15.68 Sum 5168.09 1935.00 3201.35 63881.82 3208.00 714.94 Count 88 88 88 88 88 88

In this section, we estimate the 95% confidence interval for the two variables (one under water and sanitation while the other under Access to advanced education).

Under this we considered access to improved sanitation facilities. The 95% confidence estimation is given as follows;

CI:

, ,

CI:

CI:

Lower bound:

Lower bound:

From the above calculations, we are 95% confident that the true mean of access to improved sanitation facilities is between 52.3992 and 65.0608.

Under this we considered Women's average years in school. The 95% confidence estimation is given as follows;

From the above calculations, we are 95% confident that the true mean of Women's average years in school is between 7.3164 and 8.9236.

This section sought to carry out different hypothesis tests.

The first hypothesis that we tested was on whether there is evidence of significant differences in the Women's average years in school. The following hypothesis was tested at 5% level of significance.

H0: The women’s average years in school is not different for the American countries and African countries.

H1: The women’s average years in school is not different for the American countries and African countries.

This was tested at 5% level of significance and the results are presented below;

 t-Test: Two-Sample Assuming Equal Variances Africa America Mean 5.78413 11.23435 Variance 7.371243 4.346289 Observations 46 23 Pooled Variance 6.377974 Hypothesized Mean Difference 0 df 67 t Stat -8.45066 P(T<=t) one-tail 1.85E-12 t Critical one-tail 1.667916 P(T<=t) two-tail 3.71E-12 t Critical two-tail 1.996008

An independent samples t-test was performed to compare the mean women’s number of years in school for the African and American countries. Results showed that the African countries (M = 5.78, SD = 2.72, N = 46) had significant difference in terms of the mean women’s number of years in school when compared to the American countries (M = 11.23, SD = 2.08, N = 23), t (67) = -8.45, p < .05, two-tailed. The difference of 5.45 showed a significant difference.  Essentially results showed that the level of Access to Advanced Education is higher among American countries than African countries.

The second hypothesis that we tested was on whether there is evidence of significant differences in terms of Personal Safety between Asian and American countries. The following hypothesis was tested at 5% level of significance.

H0: The average traffic deaths is not different for the Asian countries and American countries.

H1: The average traffic deaths is significantly different for the Asian countries and American countries.

This was tested at 5% level of significance and the results are presented below;

 t-Test: Two-Sample Assuming Equal Variances American Asian Mean 16.15217 15.59474 Variance 30.37988 49.73053 Observations 23 19 Pooled Variance 39.08767 Hypothesized Mean Difference 0 df 40 t Stat 0.287602 P(T<=t) one-tail 0.387568 t Critical one-tail 1.683851 P(T<=t) two-tail 0.775136 t Critical two-tail 2.021075

An independent samples t-test was performed to compare the mean traffic deaths for the American and Asian countries. Results showed that the American countries (M = 16.15, SD = 5.51, N = 23) had no significant difference in terms of the mean traffic deaths when compared to the Asian countries (M = 15.59, SD = 7.05, N = 19), t (40) = 0.29, p > .05, two-tailed. The difference of 0.56 showed no significant difference.  Essentially results showed that there is no significant difference in terms of Personal Safety between Asian and American countries.

## Traffic Deaths

The third hypothesis that we tested was on whether there is evidence of significant differences in terms of Environmental Quality between African and American countries. The following hypothesis was tested at 5% level of significance.

H0: The average Greenhouse gas emissions is not different for the African countries and American countries.

H1: The average Greenhouse gas emissions is significantly different for the African countries and American countries.

This was tested at 5% level of significance and the results are presented below;

 t-Test: Two-Sample Assuming Equal Variances Africa American Mean 975.1168 434.2134 Variance 2481308 49631.49 Observations 46 23 Pooled Variance 1682847 Hypothesized Mean Difference 0 df 67 t Stat 1.632735 P(T<=t) one-tail 0.053608 t Critical one-tail 1.667916 P(T<=t) two-tail 0.107216 t Critical two-tail 1.996008

An independent samples t-test was performed to compare the mean Greenhouse gas emissions for the African and American countries (Rice, 2006). Results showed that the African countries (M = 975.12, SD = 1575.22, N = 46) had no significant difference in terms of the mean Greenhouse gas emissions when compared to the American countries (M = 434.21, SD = 222.78, N = 23), t (67) = 1.63, p > .05, two-tailed. The difference of 540.91 showed an insignificant difference.  Essentially results showed that the Greenhouse gas emissions is not significantly different for the American and African countries.

The first scatter plot of Greenhouse gas emissions and access to improved sanitation facilities is given below;

As can be seen, the plot shows that a negative relationship exists between access to water and sanitation facilities and the greenhouse emissions.

This is a continuation of the correlation between access to water and sanitation and greenhouse gas emissions. The dependent variable is greenhouse gas emissions while the independent variable is the access to water and sanitation services (Tofallis, 2009). The results of the regression equation model are given below;

The value of the R-Squared is 0.0586; this means that only 5.86% of the variation in the dependent variable is explained by the independent variable in the model. The overall model was found to be significant and fit to estimate the dependent variable (p-value < 0.05).

 SUMMARY OUTPUT Regression Statistics Multiple R 0.242026 R Square 0.058576 Adjusted R Square 0.04763 Standard Error 1142.303 Observations 88

The correlation coefficient is -0.242; this means that a negative relationship exists between access to water and sanitation facilities and greenhouse gas emissions (YangJing, 2009).

 ANOVA df SS MS F Significance F Regression 1 6982302 6982302 5.351009 0.023097 Residual 86 1.12E+08 1304857 Total 87 1.19E+08
 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 1274.579 266.6122 4.78065 7.15E-06 744.5719 1804.587 Access to improved sanitation facilities -9.34216 4.038588 -2.31322 0.023097 -17.3706 -1.31371

The estimated regression model is;

The value of the coefficient (slope) for the access to water and sanitation facilities is -9.3422; this means that an increase in the access to water and sanitation facilities would result to a decrease in greenhouse gas emissions.

The p-value for the coefficient of access to improved sanitation facilities is 0.023 (a value less than 5% level of significance). This means that the variable is significant in the model and that a linear relationship exists between access to water and sanitation facilities and greenhouse gas emissions.

## Press Freedom Index

As can be seen, the plot shows that a negative relationship exists between corruption and the Press freedom Index. This means that an increase in the Press Freedom Index would result to a reduction in corruption index.

This is a continuation of the correlation between corruption and press freedom index. The dependent variable is corruption while the independent variable is the press freedom index. The results of the regression equation model are given below;

The value of the R-Squared is 0.1858; this means that only 18.58% of the variation in the dependent variable is explained by the independent variable in the model (Good & Hardin, 2009). The overall model was found to be significant and fit to estimate the dependent variable (p-value < 0.05).

 SUMMARY OUTPUT Regression Statistics Multiple R 0.431102 R Square 0.185849 Adjusted R Square 0.176382 Standard Error 13.29739 Observations 88

The correlation coefficient is -0.4311; this means that a negative relationship exists between corruption and press freedom index.

 ANOVA df SS MS F Significance F Regression 1 3471.248 3471.248 19.63147 2.75E-05 Residual 86 15206.57 176.8206 Total 87 18677.82
 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 51.79927 3.742106 13.84228 1.34E-23 44.36021 59.23833 Press Freedom Index -0.4218 0.095199 -4.43074 2.75E-05 -0.61105 -0.23255

The value of the coefficient (slope) for the access to water and sanitation facilities is -0.4218; this means that an increase in the press freedom index would result to a decrease in corruption cases (Armstrong, 2012).

The p-value for the coefficient of press freedom index is 0.000 (a value less than 5% level of significance). This means that the variable is significant in the model and that a linear relationship exists between press freedom index and corruption cases.

Conclusion

This study sought to investigate and understand the social progress index data for 2017. The study considered 6 different categories for analysis purposes. The categories are;

• Category 2: Water and Sanitation
• Category 4: Personal Safety
• Category 8: Environmental Quality
• Category 10: Personal Freedom and Choice

Three different hypothesis were tested. The first hypothesis tested whether there is evidence of significant differences in the Women's average years in school. Results showed that the Women's average years in school is higher among American countries than African countries. The second hypothesis tested whether there is evidence of significant differences in terms of traffic deaths between Asian and American countries. Results showed that there is no significant difference in the traffic deaths between Asian and American countries. The last hypothesis tested whether there is evidence of significant differences in terms of greenhouse gas emissions between African and American countries. Results showed that the Greenhouse gas emissions is not significantly different for the American and African countries.

In terms of limitations, this study only utilized the 2017 dataset. This makes it hard to gauge whether the influence obtained is as a result of a particular change within the year. Next study should attempt to use a panel data where different years are taken into consideration so as to ascertain that the change is not sudden.

References

Armstrong, J. S., 2012. Illusions in Regression Analysis. International Journal of Forecasting (forthcoming), 28(3), p. 689.

Good, P. I. & Hardin, J. W., 2009. Common Errors in Statistics.

Rice, J. A., 2006. Mathematical Statistics and Data Analysis.

Tofallis, C., 2009. Least Squares Percentage Regression. Journal of Modern Applied Statistical Methods, 7(6), p. 526–534.

YangJing, L., 2009. Human age estimation by metric learning for regression problems. International Conference on Computer Analysis of Images and Patterns, p. 74–82.

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