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Task 1: Project definition and Data Collection

In this project, the relationship between adult literacy rate and life expectancy will be evaluated. Adult literacy rate is the measure of the proportion of adults in the country with basic literacy. Life expectancy is a measure of the expected length of life for the people living in a country. Both literacy levels and life expectancy are measures of development in the country. High literacy rates are associated with higher development. Similarly, higher life expectancy is associated with higher levels of development.

In this study, life expectancy is the dependent variable while literacy rate is the independent variable. We shall evaluate the relationship between the two variables by using both descriptive and inferential statistics. The measures of central tendency, dispersion as well as correlation and regression analysis will be used in the study.

The data for the study is collected from www.gapminder.org. A sample of African and Middle East countries is then selected for the study. The study sample consists of 61 countries from the two regions. The data collected contains the two variables. Both variables are quantitative data measured on the ratio scale. Most of the selected countries from both regions represent data for developing countries. However, all the countries do not have uniform levels of development.

Task 2.1: Data Analysis

We shall carry out a regression analysis on the dataset to determine the impact of literacy on life expectancy. First, we need to determine whether there is a linear relationship between the dependent variable and the independent variable. The scatter plot below shows the relationship between the two variables.

There is a linear relationship between literacy rate and life expectancy as shown above. The line of best fit is upward sloping. This shows that there is a positive linear relationship between independent variable and the dependent variable. In addition, there is likelihood of extreme low values which are likely outliers because they lie further away below the line of best fit. The outliers are caused by the existence of some countries with high literacy rate but low life expectancy or some countries with low literacy rate but high life expectancy.

The equation for the line of best fit obtained is shown below.

Y = 0.2056X + 51.879

Where Y is life expectancy and X is literacy rate.

The above regression equation is determined using the following fomrulas.

a = {(Σy)(Σx2) – (Σx)(Σxy)} / {n(Σx2) – (Σx)2}

b = {n(Σxy) – (Σx)(Σy)} / (Σx)2

Where the linear regression equation is of the form,

Y = a + bx where a is the y-intercept and b is the slope of the equation.

a = {(4017.76*305902.7259) – (4149.288*278158.1616)} / {(61*305902.7259) – 4149.2882}

a = 74,885,413.98 / 1,443,475.373 = 51.8786

b = {(61*278158.1616) – (4149.288*4017.76)} / {61*305902.7259 – 4149.2882

b = 296,804.5027 / 1,443,475.373 = 0.2057

From the above calculations, the regression equation is Y = 51.8786 + 0.2057 X

We need to determine the Pearson’s Product moment correlation coefficient, r for the relationship between the dependent variable and the independent variable. The value of r obtained from the excel formula is 0.5164. The formula below will be used to calculate the value of r.

r = {nΣxy – ΣxΣy} / √{[nΣx2 – (Σx)2]*[nΣy2

– (Σy)2} = (61*278158.1616) – (4149.288*4017.76) / √[(61*305902.7259) – 4149.2882][(61*268381.6826) – 4017.762]

r = 296,804.5027 / 574,798.2835 = 0.5164

Task 2.2: Data Grouping

The maximum life expectancy for the sampled countries is 82.91 years while the minimum life expectancy is 48.86 years. The range for life expectancy is 34.05. Using the value of range above, we create the following frequency table of 12 groups with a class interval of 3 years. The table below represents the frequency for the 12 groups.

Group

Frequency

48 - 51

1

51 - 54

3

54 - 57

1

57 - 60

7

60 - 63

15

63 - 66

10

66 - 69

5

69 - 72

4

72 - 75

5

75 - 78

4

78 - 81

5

81 - 84

1

Using the above table, we can create the following histogram.

The figure below shows the ogive for the above distribution.

The table below shows the calculation of the angle for pie chart.

Group

Frequency

Cumulative frequency

Angle

Angle size

48 - 51

1

1

(1/61)*360

5.901639

51 - 54

3

4

(3/61)*360

17.70492

54 - 57

1

5

(1/61)*360

5.901639

57 - 60

7

12

(7/61)*360

41.31148

60 - 63

15

27

(15/61)*360

88.52459

63 - 66

10

37

(10/61)*360

59.01639

66 - 69

5

42

(5/61)*360

29.5082

69 - 72

4

46

(4/61)*360

23.60656

72 - 75

5

51

(5/61)*360

29.5082

75 - 78

4

55

(4/61)*360

23.60656

78 - 81

5

60

(5/61)*360

29.5082

81 - 84

1

61

(1/61)*360

5.901639

The pie chart below shows the distribution of life expectancy among the groups.

We can use the table below to calculate the mean median, mode, standard deviation and interquartile range.

Group

x

Frequency(f)

Cumulative frequency

fx

fx^2

48 - 51

49.5

1

1

49.5

2450.25

51 - 54

52.5

3

4

157.5

8268.75

54 - 57

55.5

1

5

55.5

3080.25

57 - 60

58.5

7

12

409.5

23955.75

60 - 63

61.5

15

27

922.5

56733.75

63 - 66

64.5

10

37

645

41602.5

66 - 69

67.5

5

42

337.5

22781.25

69 - 72

70.5

4

46

282

19881

72 - 75

73.5

5

51

367.5

27011.25

75 - 78

76.5

4

55

306

23409

78 - 81

79.5

5

60

397.5

31601.25

81 - 84

83.5

1

61

83.5

6972.25

Sum

61

4013.5

267747.25

Mean = Σfx / n = 4013.5 / 61 = 65.80 years.

Mode = the modal class is 60 – 63 years.

Median = 63 + [(30.5 – 27)/10]*3 = 63 + 1.05 = 64.05

Standard deviation = √{Σfx2 – (Σfx)2/n}/n-1 = √[267747.25 – (4013.52/61)] / 60 = √61.3115

Standard deviation = 7.83

Q1 = 60 + [(15.25 – 12)/15]*3 = 60 + 0.65 = 60.65

Q3 = 69 + [(45.75 – 42)/4]*3 = 69 + 2.81 = 71.81

Interquartile range = 71.81 – 6065 = 11.16

Task 3: Analysis and Write-up

Project Definition

The objective of this project is to determine the relationship between life expectancy and literacy rate. One of the roles of the government is to ensure high standards of living for the citizen. Although it is difficult to measure and quantify the standards of living, several parameters may be used as proxies. For example, the life expectancy of a country is an indication of the standards of living and the general social and economic welfare of the citizens. Countries with higher life expectancy rank higher on economic welfare and development than the countries with lower life expectancy (Cervellati & Sunde, 2009).

Therefore, it is important for the government and other stakeholders to review and evaluate ways of increasing the life expectancy of the citizens. However, the challenge is that the government does not have direct control on life expectancy. The only way this can be increased is through manipulation of other social and economic aspects of the citizens. One of the factors that may influence life expectancy is education. When more citizens of a country are educated, the general welfare of the community improves. Therefore, it is important for the government to determine the impact that education has on the life expectancy of the citizens. The following hypotheses will be tested in the project.

Null hypothesis: Literacy rate is not a significant predictor of life expectancy.

Alternative hypothesis: Life expectancy is a significant predictor of life expectancy.

The research question for this project is; Does literacy rate have a significant impact on life expectancy?

Data Collection

Secondary data is obtained from online sources. The data for the study is obtained from www.gapminder.org. The raw data is then recorded. A non-probability sample is then obtained from the data comprising of global report of all countries. A convenience sample of African and Middle East countries is selected. The sample is made up of 61 countries. Two variables are recorded which include the literacy rate and life expectancy.

Literacy rate is a continuous quantitative variable measured on the ratio scale. It represents the percentage of adult citizens aged above 15 years and with at least primary level of education that is crucial for using written word. Therefore, the literacy rate represents the proportion of adult population hat is able to read and communicate in written text. Literacy level provides an indication of the education system of schools and adult literacy centers. The measure for literacy level ranges between zero and 100%.

On the other hand, life expectancy is a continuous quantitative variable that is measured on the ratio scale. It represents the number of years that a new born child in the country is expected to live under the current conditions. Therefore, citizens of countries with higher life expectancy are expected to live longer on average than the citizens of countries with shorter life expectancy. Life expectancy changes over time depending on some social, human, political and environmental factors. The following hypotheses will be tested to answer the research question.

Null hypothesis 1: There is no significant relationship between literacy level and life expectancy.

Null hypothesis 2: Literacy rate does not significantly influence life expectancy.

Null hypothesis 1 will be tested using correlation analysis. The correlation coeffect will indicate the direction of the relationship as well as the size of the relationship. Null hypothesis 2 will be tested using regression analysis. The coefficients of the regression will provide the quantitative impact that literacy rate has on life expectancy. Excel will be used to analyze the data.

Analysis

Both descriptive and inferential statistics will be used to analyze the data. The table below shows the descriptive statistics of the two variables.

X

Y

Mean

68.02111

Mean

65.86492

Standard Error

2.542727

Standard Error

1.012524

Median

71.29051

Median

64.91

Mode

#N/A

Mode

61.4

Standard Deviation

19.85933

Standard Deviation

7.908065

Sample Variance

394.3932

Sample Variance

62.53749

Kurtosis

-0.69131

Kurtosis

-0.51785

Skewness

-0.4954

Skewness

0.298781

Range

70.97599

Range

34.05

Minimum

25.30775

Minimum

48.86

Maximum

96.28374

Maximum

82.91

Sum

4149.288

Sum

4017.76

Count

61

Count

61

The average literacy rate for the sampled countries is 68.02% with a standard deviation of 19.86%. The maximum literacy rate is 96.28% while the minimum literacy rate is 25.31%. The average life expectancy is 65.86 years with a standard deviation of 7.91 years. The maximum life expectancy is 82.91 years while the minimum life expectancy is 48.86. We need to determine whether the sample data complies with the assumptions of linear regression. There should be a linear relationship between the independent and dependent variables. In addition, the variables should be quantitative without outliers. The dependent variable should also be normally distributed (Witte & Witte, 2015). The histogram below shows the distribution of the dependent variable.

The histogram shows that the dependent variable is normally distributed with positive skewness. The graph below shows the relationship between the variables.

The scatter plot above shows that there is a linear relationship between the dependent variable and the independent variable.

Next, we carry out a correlation analysis to determine the correlation between the dependent and independent variables. The table below shows the results of the correlation analysis.

X

Y

X

1

Y

0.516365

1

The correlation coefficient is 0.5164. This shows that 51.64% of the changes in life expectancy ca be explained by the changes in literacy rate. In addition, both variables are positively correlated.

The table below shows the results of the regression analysis.

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

51.87851

3.143887

16.50139

8.9E-24

45.5876

58.16941

X

0.205619

0.044396

4.631508

2.05E-05

0.116783

0.294454

The regression equation obtained from the analysis is Y = 51.8785 + 0.2056x

Data Interpretation

The regression equation implies that when literacy rate is at 0%, the life expectancy is 51.87 years. When literacy rate increases by 1%, life expectancy increased by 0.2056 of a year. The coefficient for the independent variable is significant because the p-value is lower than significance level, t = 4.63, p-value = 2.05E-05. Therefore, literacy rate is a significant predictor of life expectancy. Therefore, an increase in literacy rates can increase the life expectancy of the citizens. The government can increase life expectancy of the citizens by promoting the ease of access to schools and education institutions.

The correlation coefficient is relatively low. This implies that there are other variables that may influence the life expectancy of the citizens like access to health care, climate, etc. therefore, the government should seek t evaluate more factors that have significant effects on life expectancy.

Conclusion

The research question for the project was analyzed and evaluated. The research findings reveal that there is a positive relationship between literacy rate and life expectancy. Thus, the government can increase life expectancy by promoting policies that improve literacy rates. However, the findings of this study assume that the correlation between the two variables is an indication of causality. This may not be the case. The positive correlation for the two variables may be because of the presence of confounding variables that cause the two variables to change in the same direction (Tokunaga, 2016). In this case, the government would not have control of life expectancy by influencing literacy rate. In addition, the results of the project may not be reliable because the sampling method used does not follow probability. Therefore, the findings may be influenced by sampling bias. The findings of the study are limited to the geographical areas in which the sample was collected. The findings may not be generalized into the world population because the sample is based on African and Middle East countries. It is therefore important for further study to be contacted to include a global sample frame.

Bibliography

Cervellati, M. & Sunde, U., 2009. Life expectancy and economic growth: the role of the demographic transition. London: Centre for Economic Policy Research.

Tokunaga, H., 2016. Fundamental statistics for the social and behavioral sciences. Los Angeles: Sage.

Witte, R. S. & Witte, J. S., 2015. Statistics. Hoboken: John Wiley and Sons, Inc..

Appendix

Table 1: Multiple correlation for regression analysis

Regression Statistics

Multiple R

0.516365

R Square

0.266633

Adjusted R Square

0.254203

Standard Error

6.829368

Observations

61

Table 2: Analysis of variance for regression model.

ANOVA

df

SS

MS

F

Significance F

Regression

1

1000.474

1000.474

21.45087

2.05E-05

Residual

59

2751.775

46.64026

Total

60

3752.25

September 25, 2023

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