The Global Social Mobility Report 2020 ranked Singapore 20th out of 82 countries studied. After reading the report, Mr. Tan, a student at the Singapore University of Social Sciences, was interested to estimate income mobility across generations in Singapore. He surveyed a random sample of 120 students from the Singapore University of Social Sciences, and collected data on monthly income of their father and their oldest sibling who is currently working in 2021. He managed to get 72 pairs of income data, which are given in the Excel data file "BUS105_mobility". Based on his observation, he hypothesized that rich children have rich fathers.

Question 1 (a) Describe the 90% confidence interval of the mean monthly income of children and fathers in 2021, respectively. Interpret and discuss whether Mr. Tan can conclude that the mean monthly income of fathers is higher than that of children. Please round your answer to zero decimal places. (20 marks)

(b) Apply an appropriate hypothesis test to determine if the mean monthly income of fathers is higher than that of children, at the significance level of 10%. Examine the assumptions required to perform the test. Are these assumptions reasonable? Please provide explanations. (30 marks)

(c) To examine whether rich children have rich fathers, Mr. Tan learnt from his seniors that he can test whether the coefficient of correlation (r) is greater than 0. He did some research and found that the test statistic ist=1r2rn2 which follows the Student's tdistribution with (n-2) degrees of freedom. Please help Mr. Tan to complete the analysis. Explain your results. (20 marks)

(d) Criticise the analysis done by Mr. Tan by identifying two (2) concerns. If you have a free hand to study this research question starting from data collection to analysis, explain how you would conduct the project. Summarise the above analysis in a simplified report. Keep your answer within 500 words and indicate your word count at the end of your answer. (30 marks)