assignment marking guide

Assignment STA117 2012/S1

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Faculty of Management and Computing

MARKING GUIDE

Business Mathematics

STA117

Assignment

Due date: 15th April 2012 (2p.m.)

Objectives

Demonstrating an understanding of descriptive statistics by accurately representing data

by means of graphs, charts, tables, etc.

Extending the knowledge of the subject by researching topics which are within the "zone

of proximal development" of the students.

Making inferences about a given set of information by interpreting and analysing them

and making generalisations in the context of the scenarios given.

Independent learning and application of knowledge of statistics to new topics to

demonstrate the ability of the students to learn new topics related to statistics.


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1.

(a) Appropriate title 1 mark

Labelling axes 2 marks

Bars for each type of vehicle mark @ 3 marks

Appropriate scale (must cover at least two-thirds of a graph sheet or done using a

computer program such as MS Excel to represent the information appropriately)

mark

(b) 1 mark for each valid point OR award 3 marks in full for a concise explanation

The variable is categorical (qualitative)

Cannot assign numbers in a meaningful way

There is no continuity (for e.g. a pick-up truck does not evolve itself into a motorbike,

etc.

(c) Any 2 possible types of vehicles (e.g. Jeeps, Cars(belonging to the government),

wheel barrows,...etc) 2 marks

(d) YES 1 mark

It is unusual for any data collected to have a very large value for other category.

This could be a failure on the part of designing the questionnaire or survey form. It is

quite possible to have another category with sufficient numbers of vehicles. 1 mark

(7 + 3 + 2 + 2 = 14 marks)


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2. The table below shows the rankings given by 2 judges to 10 different brands of tea.

Rank J1 Rank J2 d d2

7 3 4 166 2 4 164 7 -3 98 1 7 499 4 5 25

10 5 5 253 8 -5 251 9 -8 645 6 -1 12 10 -8 64

294SUM

(a) Correct values of d 3 marks (Deduct for each incorrect value up to a maximum

of 3)

(b) Correct values of d2 2 marks

(c) Correct 1 mark

(d) = 0.7818 4 marks (b) Preference for tea (what the judges consider to be tasty or not) are considerably different. As

the correlation is negative, it indicates that a brand of tea that is championed by Judge A will not

be liked at all by judge B and vice versa. 2 marks

(10 + 2 = 12 marks)


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3. (a) Visit http://www.random.org and click on numbers --> integers. 2 marks

Generate 60 random integers. Each integer should have a value between 1 and 6. 2 marks Format in 10 columns 2 marks Click on "Get Numbers" 2 marks Take a print screen of the list of numbers. 2 marks Award full 10 marks if the screen shot of random numbers list is correct.

(b) Award 1 mark for each correct frequency 6 marks

(c) Carried out a proper Chi-squared test by taking the differences between observed

(values generated from www.random.org and expected frequencies (10 each since it is a

simulation of a die being rolled 60 times).

Null Hypothesis

: The numbers generated follow a discrete uniform distribution

Alternative Hypothesis

: The numbers generated does not follow a discrete uniform distribution

Identifying observed and expected values correctly mark

Correct null and alternative hypothesis 2 marks

Degree of freedom = 5 mark

Correct Chi-squared value (must be less than 11.07) 2 marks

Conclusion do not reject 1 mark

(d) The numbers generated are truly random. This may be a proper representation of (for

example) a simulation of a fair die. 2 marks

(10 + 6 + 6 + 2 = 24 marks)

TOTAL MARKS = 50

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