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. Source: https://www.weforum.org/reports/global-social-mobility-index-2020-why-economies-benefit-from-fixing-inequality/

No	income_child	income_father
1	2100	900
2	1200	1200
3	4500	4770
4	2700	3180
5	3000	2385
6	4500	6360
7	4500	4770
8	3000	15900
9	1500	1590
10	2520	4770
11	4500	11130
12	4500	4770
13	1500	7950
14	4500	4770
15	3000	3180
16	1200	1908
17	3750	5088
18	3000	6010
19	2850	3498
20	3750	6360
21	2700	3975
22	4500	7950
23	1500	9540
24	3150	3180
25	3000	3180
26	3000	3180
27	2250	2385
28	1500	3180
29	4500	4770
30	4500	1590
31	1200	1908
32	3000	4770
33	1800	3975
34	4500	4770
35	3000	3180
36	2250	4770
37	750	954
38	1800	6000
39	3000	1500
40	630	600
41	600	600
42	2400	2400
43	600	600
44	4500	1500
45	450	450
46	1500	1500
47	2400	1800
48	300	600
49	900	900
50	900	300
51	1200	1500
52	1710	900
53	240	360
54	3000	3300
55	1800	2400
56	1500	1200
57	2400	1350
58	1500	450
59	1800	150
60	3600	1050
61	600	900
62	360	750
63	900	900
64	6000	3600
65	2400	1200
66	600	600
67	6000	6000
68	1500	1500
69	1500	2400
70	450	900
71	150	180
72	3000	3000

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. (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. (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 is =212 which follows the Student's t-distribution with (n-2) degrees of freedom. Please help Mr. Tan to complete the analysis. Explain your results. (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.