THREE (20 Marks) A research team comprising a paediatrician and a health economist wants to establish whether there is an association between a babys birth weight and the level of wealth of the family into which the baby is born. Using the annual gross income of families as proxy for wealth, they hypothesised that the birth weights of children born into wealthy families are greater than the birth weights of children born into less wealthy families. Table 3.1, below, is a record of a random sample of the birth weights of 15 children delivered at a Johannesburg hospital during the month of November 2022 and the gross incomes of the childrens families: Table 3.1: A sample of the birth weights and gross family income of 15 babies delivered at a Johannesburg hospital during the month of November 2022 Baby Number Birth Weight (kg) Gross Family Income (R 000) 1 2.5 120 2 2.7 150 3 2.7 153 4 3.6 182 5 2.8 150 6 2.9 156 7 5.4 450 8 3.1 200 9 3.5 240 10 3.3 180 11 3.2 200 12 3.5 250 13 3.6 250 14 3.6 200 15 5.0 320 Using the IBM SPSS Statistics version 25, the researchers analysed the data and the output depicted in Figure 3.1 to Figure 3.3 was generated: Figure 3.1 Correlations (Parametric) Birth_Weight Gross_ Family_Income Birth_Weight Pearson Correlation 1.000 .947 ** Sig. (2-tailed) .000 N 15 15 Gross_ Family_Income Pearson Correlation .947** 1.000 Sig. (2-tailed) .000 . N 15 15 **. Correlation is significant at the 0.01 level (2-tailed). Figure 3.2 Correlations (Non-parametric) Birth_Weight Gross_ Family_Income Spearman's rho Birth_Weight Correlation Coefficient 1.000 .879 ** Sig. (2-tailed) . .000 N 15 15 Gross_ Family_Income Correlation Coefficient .879** 1.000 Sig. (2-tailed) .000 . N 15 15 **. Correlation is significant at the 0.01 level (2-tailed). Figure 3.3 Scatter plot Required: 3.1.Identify the independent variable (IV) and dependent variable (DV) used in the study. (2 marks) 3.2. What are the levels of measurement of the independent variable (IV) and dependent variable (DV)? (2 marks) 3.3.What does the scatter plot (Figure 3.3) suggest about the relations between Family wealth and Birthweight? (2 mark) 3.4.Uncertain if the data met the requirements for parametric tests, the researchers opted for both Pearsons correlation coefficient and Spearmans rho in a correlational analysis of the data. The outputs of the Pearsons r and Spearmans rho are depicted in Figure3.1 and Figure 3.2, respectively. 3.4.1. Identify THREE (3) assumptions of parametric tests. (3 marks) 3.4.2.Suppose that the researchers decide not to test the data for parametric assumptions, can they conclude, on the basis of the outputs of the correlation analysis ONLY, that there exists a significant, strong, positive correlation between Family wealth and Birthweight? Explain. (5 marks) 3.4.3.Does the conclusion in 3.4.2 in any way dispel any notion of causal ambiguity between family wealth and birthweight? (2 marks) 3.4.4.Discuss any TWO (2) major weaknesses of the study and suggest relevant ways to address them. (4 marks)