In November 2021, the government accepted the progressive wage proposal for the security sector which sets the monthly gross salaries of entry-level security officers to a minimum of S$3,530 by 2028. The current minimum monthly gross salary of entry-level security officers is $1,400 in 2021. Compare the expected change of minimum monthly salary of entry-level security officers to the income trends discussed above. Comment on the progressive wage model (hint: the pros and concerns related to the progressive model). (9 marks)

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You must answer ALL the questions. (Total 100 marks)

Question 1

Table 1 shows the median gross monthly income from work (including employer CPF contributions) of full-time employed residents for 2011-2021.

Table 1-1: Median gross monthly income from work of full-time employed residents

Median gross monthly income ($)

2011

3,249

2012

3,480

2013

3,705

2014

3,770

2015

3,949

2016

4,056

2017

4,232

2018

4,437

2019

4,563

2020

4,534

2021

4,680

Source: Ministry of Manpower, Singapore.

Calculate the average annual change in median gross monthly income for the period 2011-2016 and 2016-2021, respectively.

(4 marks)

Calculate the cumulative change in median gross monthly income for the period 2011-2016 and 2016-2021, respectively.

(4 marks)

Discuss your observations on the income trends in the past decade, based on your answers to part (a) and (b), as well as some graphic representation.

(8 marks)

In November 2021, the government accepted the progressive wage proposal for the security sector which sets the monthly gross salaries of entry-level security officers to a minimum of S$3,530 by 2028. The current minimum monthly gross salary of entry-level security officers is $1,400 in 2021. Compare the expected change of minimum monthly salary of entry-level security officers to the income trends discussed above. Comment on the progressive wage model (hint: the pros and concerns related to the progressive model).

(9 marks)

Timed Online Assignment – January Semester 2022

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Question 2

Dr. Tan has taught BUS105 many years, and he knows that around 75% of students will read the study guide. Among those who read the study guide, 87% will pass the course. Among students who did not read the study guide, 65% will pass the course.

Identify the probability that a student will pass BUS105.

(5 marks)

Raymond took BUS105 last semester, and he passed BUS105. What is the probability that he had read the study guide?

(7 marks)

Statistics show that the distribution of monthly rent for a 4-room HDB flat has a mean of $2,530 and a standard deviation of $240.

Assume that the distribution of monthly rent for a 4-room HDB flat follows a normal distribution, what is the probability of renting a flat at a price cheaper than $2,000?

(5 marks)

In fact, the distribution of monthly rent for a 4-room HDB flat is positively skewed. What is the probability of finding the mean rent of a sample of 35 units of 4-room HDB flat more than $2,600?

(8 marks)

Question 3

In Kisi’s Global Work-Life Balance Index 2021, Hong Kong, Singapore and Bangkok were ranked the top three cities with the most overworked populations in the world. Mr. Tan, the HR director of a multi-national computer software company, is interested to find out whether the working hours of executives in the three offices of his company are the same or not. To do so, he selected a sample of 8 executives from their Hong Kong, Singapore and Bangkok offices, and collected the number of hours worked per week in Table 3-1.

Table 3-1: Weekly working hours in three offices

Hong Kong

Singapore

Bangkok

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Timed Online Assignment – January Semester 2022

Calculate the 95% confidence intervals of the mean weekly working hours in the Hong Kong and Singapore offices. Discuss whether there is a difference in the working hours in the two offices? You are required to show relevant Excel table.

(9 marks)

Apply an appropriate hypothesis test at the 5% significant level to determine whether the mean weekly working hours of executives in the three offices are the same. You are required to write down the five steps carefully and show relevant Excel table.

(10 marks)

Can you believe your findings in question (b)? (hint: consider the assumptions of the ANOVA test)

(6 marks)

Question 4

Climate change is a global challenge, and many countries have committed to reduce carbon emissions significantly before 2050. To understand the determinants of carbon dioxide emissions, Mr. Tan collected data on CO2 emissions (million tons), GDP (billion US$), population (million), energy use per capita (kg of oil equivalent), and share of electricity production from oil, gas and coal sources, in 2015 from 34 countries from World Development Indicators, and performed the regression analysis. The data can be found in the “TOA_DATA” file.

Describe the relationship between the CO2 emissions and the four (4) independent variables by writing down the linear equation. Interpret the coefficients to show how each of the independent variables impact CO2 emissions. You are required to show the regression output from Excel.

(7 marks)

Mr. Tan wants to estimate the CO2 emissions in country S in 2020. He found GDP is 340 billion USD, population is 5.686 million, per capita energy use is 7,800 kg of oil equivalent, and electricity production from oil, gas and coal sources accounts for 95%. What is your estimate of CO2 emissions in country S?

(3 marks)

Execute appropriate hypothesis tests to advise Mr. Tan which variable is significant at the 10% significance level. You are required to write down your steps carefully.

(9 marks)

Discuss three (3) statistical concerns in the estimation of CO2 emissions in country S in 2020 in part (b).

(6 marks)

—– END OF PAPER —–

Timed Online Assignment – January Semester 2022

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