# BUS105: Dr. Tan has taught BUS105 for many years, and he knows that around 75% of students will read the study guide: Statistics Home Work, SUSS

Question 1

Dr. Tan has taught BUS105 for 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.

a) Identify the probability that a student will pass BUS105.
b) Raymond took BUS105 last semester, and he passed BUS105. What is the probability that he had read the study guide?

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.

a) 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?
b) 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 flats more than \$2,600?

Question 2

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

Table 2-1: Median gross monthly income from work of full-time employed residents

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Calculate the average annual change in median gross monthly income for the
period 2011-2016 and 2016-2021, respectively.
Calculate the cumulative change in median gross monthly income for the period 2011-2016 and 2016-2021, respectively.
Discuss your observations on the income trends in the past decade, based on your answers to parts (a) and (b), as well as some graphic representation.
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 in the minimum monthly salary of entry-level security officers to the income trends discussed above. Comment on the progressive wage model

Question 3

In Kisi’s Global Work-Life Balance Index 2021, Hong Kong, Singapore, and Bangkok have ranked as 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 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

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 the relevant Excel tables.
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 the relevant Excel table.
Can you believe your findings in question (b)? (hint: consider the assumptions of the ANOVA test).