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BUS105e

Examination – January Semester 2015

Statistics

Thursday, 14 May 2015

10:00 am – 12:00 pm

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Time allowed: 2 hours

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INSTRUCTIONS TO STUDENTS:

1. This examination contains FOUR (4) questions and comprises TWENTYEIGHT (28) printed pages (including cover page, Appendices A and B).

2. You must answer ALL questions.

3. This is closed book examination.

4. All answers must be written in the answer book.

At the end of the examination

Please ensure that you have written your examination number on each answer book

used.

Failure to do so will mean that your work cannot be identified.

If you have used more than one answer book, please tie them together with the string

provided.

THE UNIVERSITY RESERVES THE RIGHT NOT TO MARK YOUR

SCRIPT IF YOU FAIL TO FOLLOW THESE INSTRUCTIONS.

BUS105e Copyright © 2015 SIM University

Examination – January Semester 2015

Page 1 of 28

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

Question 1

Demographic statistics are important for various aspects of social planning and

organisation. For instance, the general fact that Singapore has low fertility rate - 1.19 in

2013 compared with a commonly recognised benchmark replacement rate of 2.1 features significantly in policy debates on immigration and economic development.

For Question 1, you will refer to Appendix A which contains an abstract of The United

Nations’ World Population Prospects: The 2012 Revision for data on global

demographic estimates and projections.

(a)

Describe the population size and the male-to-female ratio of Singapore in 2013.

Compare these statistics with those from the countries with the biggest

(reported) and the smallest (reported) male-to-female ratios.

(6 marks)

(b)

Discuss how data pertaining to population sizes and male-to-female ratios may

be collected. How accurate do you think is the data?

(6 marks)

(c)

From Table S.2 Total Population by Country, the following diagrams are

produced with data selected from the years 2013 and 2025.

BUS105e Copyright © 2015 SIM University

Examination – January Semester 2015

Page 2 of 28

Name the type of statistical chart that is common to both diagrams. Explain why

the bars in the top diagram appear like lines. Interpret what the charts say about

the world population.

(6 marks)

(d)

Countries accounting for about 75 per cent of the world population for the year

2013 (Table S.3) are shown here:

BUS105e Copyright © 2015 SIM University

Examination – January Semester 2015

Page 3 of 28

The following data table is produced by the Excel data analysis tools to

summarise the statistics for these countries:

Explain why the mean is so much bigger than the median and comment on the

shape of the chart with reference to the world population situation using the data

as shown in the table above.

(7 marks)

Question 2

(a)

A survey is conducted with 100 Singaporeans on their favourite car brands by

students in the Statistics 101 class. They tabulated the collected data as follows:

Brand

Mercedes

Toyota

BMW

Mazda

Others

Percentage

17.5%

35%

13%

28%

x%

(i)

Comment on the validity of the numerical figures shown under the

Percentage column. Correct any error that you may detect.

(ii)

Taking into account your answer in (i), identify the value of x if the

percentages shown are interpreted as the probabilities of favourite cars

when a Singaporean is randomly asked.

(iii)

Identify the probability that a random favourite car response is BMW or

Mercedes.

(iv)

Identify the probability that a random favourite car response is...