Note: This is a
sample exam only.
Do not treat it as
an exact indication
of any future exam.
DEAKIN UNIVERSITY
Faculty of Business and Law
School of Information Systems
MSQ791 – DATA ANALYSIS FOR MANAGERS
SAMPLE EXAMINATION PAPER
Question
1.
Mark
2.
3.
4.
5.
6.
7.
8.
9.
10.
Total
Instructions for candidates:
1.
Answer questions in the spaces provided on the question sheets. If you need more
space use the back of the page opposite the question, but only if necessary, for
example, for extra calculations. Do not use a script book.
2.
Dot/bullet point answers for written questions are acceptable.
3.
Answer ALL ten (10) questions on this Sample Exam. Show sufficient working for
each.
4.
This exam totals 100 marks and is worth 60% of the final assessment for this unit.
MSQ791 Data Analysis For Managers – Sample Exam
Page 2
QUESTION 1 (1+1+1+1+1+1+1+1+1+1) = 10 marks)
Conrobar Pty Ltd has requested you to investigate any difference in years of education of male
management staff and female management staff. The first table below gives the actual years of
education for the 14 male managers, and for the 10 female managers, in a random sample of
employees. The second table gives relevant summary measures for the two groups.
Sample data:
Males
Females
12
14
12
15
11
16
10
13
19
13
12
14
11
14
16
14
10
15
17
14
10
12
15
12
PaceXL Ungrouped Data: Years of education
Sample Data:
Number of Data Points
Minimum
Maximum
Total
Arithmetic mean
Median
Mode
First Quartile
Third Quartile
Range
Inter Quartile Range
Variance (Sample)
Standard Deviation (Sample)
Coefficient of Variation (Sample)
Skewness Coeff (Pearson's, Sample)
Males
Females
14
10
19
179
12.786
12.0
12.0
11.0
15.0
9
4.0
8.027
2.833
0.222
0.832
Find the following missing summary measures for years of education for Females.
(a)
Minimum
(b)
Maximum
(c)
Arithmetic mean
(d)
Median
(e)
Mode
(f)
First quartile
(g)
Interquartile range
(h)
Standard deviation
(i)
Coefficient of variation
(j)
Skewness coefficient
10
142
15.0
3
0.844
MSQ791 Data Analysis For Managers – Sample Exam
QUESTION 2 (1+1+1+1+1+1+1+1+1+1) = 10 marks)
Following are graphs marked A, B, C, D, E and F of six different scatterplots depicting
relationship situations between the two variables Y and X.
(cont.)
Page 3
MSQ791 Data Analysis For Managers – Sample Exam
Page 4
For the ten questions that follow, circle just one (1) of the letters given. Choose the scatterplot
which is the best example of its type or is the most appropriate for what is required. If none is
appropriate, circle the letter Z.
(a)
Perfect positive linear relationship
A B C D E F Z
(b)
No relationship with r = 0
A B C D E F Z
(c)
r = -0.79
A B C D E F Z
(d)
Curvilinear positive relationship
A B C D E F Z
(e)
Wide positive scatter
A B C D E F Z
(f)
As X increases Y tends to neither increase nor decrease
A B C D E F Z
(g)
Quadratic (parabolic) model appropriate
A B C D E F Z
(h)
R2 close to 100%
A B C D E F Z
(i)
Inverse positive relationship
A B C D E F Z
(j)
Zero linear correlation with strong relationship
A B C D E F Z
MSQ791 Data Analysis For Managers – Sample Exam
Page 5
QUESTION 3 (3+4+3 = 10 marks)
Faster Parcels, a courier service company, classifies customers by "method of payment" (for
Credit and Non-Credit customers) and by "regularity of custom" (for Regular and Non-Regular
customers).
We know the following:
(a)
70% of customers are Credit customers
60% of customers are Regular customers
40% of customers are both Regular and Credit customers
Set up a contingency table for these data by completing the following table as a "percent
of total table":
Regular
Non-Regular
Row Total
Credit
Non-Credit
Col. Total
(b)
100%
If we were to choose one customer at random, find the probabilities of each of the
following events occurring.
(i) The customer is a Credit customer.
i.e. P(Credit) =
(ii) A Regular but Non-Credit customer
i.e. P(Regular and Non-Credit) =
(iii) A Non-Credit and a Non-Regular customer
i.e. P(Non-Credit and Non- Regular) =
(iv) A Credit customer given that they are a Regular customer.
i.e. P(Credit | Regular) =
(c)
Does there appear to be any relationship between "method of payment" and "regularity of
custom". Explain your answer by using just two (2) of the results in (b) above.
MSQ791 Data Analysis For Managers – Sample Exam
Page 6
QUESTION 4 (5+5 = 10 marks)
For Faster Parcels (the courier company in Question 3), it is assumed that the delivery time for
overseas deliveries will follow a normal distribution, with a mean of 10 days and a standard
deviation of 2.5 days. Under these assumptions:
(a)
What is the probability that a parcel will be delivered within 7 to 14 days?
(b)
The company intends to offer a double refund of the freight charge for overseas
deliveries, if the delivery time is excessive. It only wants to commit itself to doing this for
1% of deliveries. What is the number of days (calculated to two decimal places) beyond
which it would have to offer this refund?
MSQ791 Data Analysis For Managers – Sample Exam
Page 7
QUESTION 5 (4+2+2+2 = 10 marks)
The Council for White Waters, a (fictitious) city in greater Brisbane with approximately 22,000
households, intends to conduct a sample survey of households to gather relevant data from
residents in regard to a range of issues pertaining to waste management planning: including
rubbish collection, non-burnable waste and recycling. The survey has great importance
because it will determine household waste management within the city for many years to come.
Data will be collected by asking households to complete an extensive questionnaire.
You are in charge of the Council’s research staff. Your research team has identified three key
stages to the decision making process.
I.
II.
III.
Data collection (including developing the questionnaire, distribution and collection).
Data processing (including coding and entering questionnaire results for computer
analysis, computer generation of relevant tables, charts, calculations, etc.).
Analysis (including interpretation of the results and presentation of findings).
A precise budget for the cost of the survey has been proposed by your team, but the Finance
Manager for the Council has insisted that there are insufficient funds available. There is no
alternative: one of these stages must be scaled back significantly.
(a)
Which of the three stages given above is the least important, and therefore the one that
you think is the most amenable to funding cuts? Provide a full explanation.
(continued)
MSQ791 Data Analysis For Managers – Sample Exam
Page 8
(b)
You have arranged to meet with the Finance Manager again, who puts the following three
suggestions to you. In each case, give your response and explanation for that response.
(i)
Abandon the pilot study for the survey.
(ii)
Replace the random sample survey of households with a sample survey of shoppers,
visitors to the local library, and visitors to the Council chambers.
(iii)
Put the survey out to tender to consultants and accept the lowest bid.
MSQ791 Data Analysis For Managers – Sample Exam
Page 9
QUESTION 6 (3+5 = 8 marks)
Following is a table containing key selected PaceXL summary measures for the annual rates
($) collected in 2005 from a random sample of households broken into low density housing (that
is, typical houses on standard sized blocks), medium density housing (that is, townhouses and
units on small blocks) and high density housing (that is, flats and apartments in multi-storey
blocks) in the City of White Waters.
PaceXL Ungrouped Data: Annual rates ($)
SAMPLE DATA
Low Density
Medium Density
High Density
Minimum
181.1
174.2
89.5
Maximum
485.5
399.9
415.0
324.5923
263.875
235.8533
283.0
241.85
219.3
Nil
206.4
Nil
232.2
206.4
159.1
Arithmetic mean
Median
Mode
First Quartile
Third Quartile
Standard Deviation
(a)
430.2
309.85
328.9
104.3829
74.2333
102.7881
The following diagram contains boxplots for annual rates for Low and High Density
Housing. Complete the diagram by drawing in the boxplot for the rates for Medium
Density Housing.
LOW
MEDIUM
HIGH
0
100
200
300
RATES ($)
400
500
MSQ791 Data Analysis For Managers – Sample Exam
(b)
Page 10
Using the graph above, and the results from the table of summary measures, write a brief
report in plain language comparing and contrasting the rates received from Low, Medium
and High density housing in 2005. (Dot point answers are acceptable.)
MSQ791 Data Analysis For Managers – Sample Exam
Page 11
QUESTION 7 (3+3+2+2 = 10 marks)
Council for White Waters eventually took a random sample of 400 households. One of the aims
of the sampling exercise is to investigate whether or not there is any difference in the amount of
household waste produced by low density housing and medium density housing. Of those
households sampled, 125 were low density housing, while 160 were medium density.
(a)
As indicated, of those sampled, 125 were low density housing. The mean amount of
household waste per week was 13.3 kilograms, with a standard deviation of 2.5
kilograms. Calculate the 99% confidence interval of weekly household waste per low
density household.
(b)
As indicated, of those sampled, 160 were medium density housing. The mean amount of
household waste per week was 12.3 kilograms with a standard deviation of 2.2 kilograms.
Calculate the 99% confidence interval of the mean value of weekly household waste per
medium density household.
(continued)
MSQ791 Data Analysis For Managers – Sample Exam
Page 12
(c)
The CEO of White Waters has insisted on maximum confidence and minimal risk, hence
the use of 99% confidence. On the basis of these two sample results, and your
subsequent confidence intervals, does there appear to be any difference in the mean
amount of weekly household waste produced by low density housing compared to
medium density housing? Explain your conclusion, and provide a recommendation you
would make to management.
(d)
Alternatively, say you wished to perform a hypothesis test as to whether or not there is
any difference in the mean amount of waste for low density housing compared to medium
density housing.
Without performing any calculations, or completing the test, what would be the null and
alternative hypotheses? (Here use Population 1 as Low Density housing, and Population
2 as Medium Density housing.) Give the hypotheses in words and in symbol form.
MSQ791 Data Analysis For Managers – Sample Exam
Page 13
QUESTION 8 (2+2+2+2+2 = 10 marks)
The White Waters Council currently receives on-going complaints about the inadequacy of the
garbage collection system. You have been asked by the Council to assess the extent of the
problem and have included an appropriate question in the survey.
The chief engineer has indicated to you that he believes that no more than 30% of households
"experience any problems". You have decided to test the validity of this figure. Of the 400
households sampled, 145 owners reported that they had "experienced problems" with the
garbage collection system. You decided to conduct an appropriate hypothesis test. Following is
the output you have generated from a statistics package. Complete the questions that follow.
PaceXL Intervals and Tests
Data Input
Significance Level (alpha) %
Ho : Proportion, p%
Sample Size, n
Sample pBar, %
Sample Count
(a)
1.0%
30.0
400
36.25
145
Test and Results
Ho : p < =
30.0
Ha : p >
30.0
Test Type :
z : Upper-tail
alpha, a :
0.01
CV of z :
2.326
Statistics:
- pBar%
36.25
- Standard Error%
2.291
- z-Statistic
2.728
- CV pBar%
35.33
- p-Value
0.0032
Conclusion:
p-Value v alpha:
- Reject Ho
Is this problem about a categorical variable or a numerical variable? Briefly explain your
answer. Include an explanation as to why the two types of variables must be treated
differently.
(continued)
MSQ791 Data Analysis For Managers – Sample Exam
(b)
Page 14
Under your test, you have set the null and alternative hypotheses as follows:
H0:
p ≤ 30%
Ha:
p > 30%
and therefore used an "upper tail" test.
Explain why you have set up the two hypotheses in this way, and why it is referred to as
an "upper tail" test.
(c)
With a hypothesis test it is usual to specify a level of significance. What level of
significance have you used in this test? On what basis would you have chosen this value,
and could other levels have been appropriate?
(continued)
MSQ791 Data Analysis For Managers – Sample Exam
(d)
Page 15
Explain the following two concepts and include calculations to show their derivations:
(i)
p (sample) % = 36.25
Calculation:
Interpretation:
(ii)
z statistic = 2.7277
Calculation:
Interpretation:
(e)
What conclusion have you come to from this test? Please explain in plain language, and
include an explanation of the reasons shy you came to this conclusion, based on the
output from your statistical test.
MSQ791 Data Analysis For Managers – Sample Exam
Page 16
QUESTION 9 (3+3 = 6 marks)
The following details are required for Q. 9 and Q. 10. Use a 5% level of significance for all tests.
Your firm manufactures microprocessors and, as production manager, you are concerned
about the proportion of defective microprocessors being produced on the production line. Each
item is tested the moment it comes off the production line, but any defectives must be thrown
away. Because of the nature of the product, there is a large defective rate. A level of up to 10%
defectives is considered to be acceptable for this product.
Demand for your firm's product is running very high, yet the factory is not large. As a result, for
the last 12 months, the company has been operating on the basis of three shifts a day, for 5
days a week. The three shifts are the Day shift (8.00 a.m. - 4.00 p.m.), the Evening shift (4.00
p.m. - 12.00 midnight.) and the Morning shift (12.00 a.m. - 8.00 a.m.). The Day shift is the
largest, in terms of staff on the production line and total output. The Morning shift is the
smallest, and run with close to the minimum number of staff to keep the production line going;
the absolute minimum is 10. While every attempt is made to keep the staff number at 15 on the
Morning shift, absenteeism is a problem on that shift.
A major concern is the proportion of defectives being produced on the Morning shift. Using data
over the past four months (equal to 90 days), you have derived the following table:
Observed Frequencies/Count
Level of
Defectives
Acceptable (10% or less)
Unacceptable (More than l0%)
Total days
(a)
Day
76
14
90
Shift
Evening
72
18
90
Morning
62
28
90
From a descriptive statistics point of view, would you say that there is any reason to
believe there is any difference in the defective rate between shifts? Explain your answer.
(cont.)
MSQ791 Data Analysis For Managers – Sample Exam
(b)
Page 17
From an inferential statistics point of view, would you say that there is any reason to
believe that there is any difference in the defective rate between shifts? To assist your
answer, the sample Chi-square statistic is 6.6857.
MSQ791 Data Analysis For Managers – Sample Exam
Page 18
QUESTION 10 (2+2+2+2+2+2+2+2 = 16 marks)
Please read this question in conjunction with the introduction from Question 9.
From a period of months, you have randomly selected 12 Morning shifts and collected the
following data, with a view to detecting any underlying factors behind the defective rate for the
Morning shift. In this problem, the dependent variable is the defective rate, measured as the
percentage that defective items are of total production.
Defective Rate
(Per cent of Total Pd’n)
%
11%
13%
8%
10%
18%
7%
10%
15%
11%
8%
11%
13%
Total Production
(Units)
380
394
280
352
375
369
410
395
406
295
367
383
Number of
Staff
on Duty
15
14
15
13
10
12
15
11
14
15
12
12
Production
Supervisor
that Shift
Smith, 0
Smith, 0
Jones, 1
Jones, 1
Smith, 0
Jones, 1
Smith, 0
Smith, 0
Jones, 1
Jones, 1
Jones, 1
Smith, 0
Minimum outside
o
Temperature C
5
10
7
6
12
8
11
7
6
8
15
9
(Note: Smith and Jones are the two production supervisors in charge of the Morning shift and
alternate on a weekly basis. In the regression model, 0 is used for Smith and 1 for
Jones.)
The data above were analysed using the Regression and Correlation routine of PaceXL,
and relevant output is reproduced below.
PaceXL: Correlation
Correlation Coefficient, r
DefRate%
DefRate%
1.000
TotalPd'n
0.493
NumStaff
-0.654
Supervisor
-0.694
MinTemp
0.300
TotalPd'n
0.493
1.000
-0.303
-0.571
0.155
NumStaff
-0.654
-0.303
1.000
0.199
-0.382
Supervisor
-0.694
-0.571
0.199
1.000
-0.120
MinTemp
0.300
0.155
-0.382
-0.120
1.000
MSQ791 Data Analysis For Managers – Sample Exam
Analysis of Variance, ANOVA
Degrees
Freedom,
df
Regression
4
Error
7
Total
11
Sum of
Squares,
SS
82.203
26.047
108.250
Mean
Square,
MS
20.551
3.721
Page 19
F-Ratio
5.523
p-Value
0.02500
p-Value
0.03530
0.97021
0.03868
0.03489
0.89252
95%
Conf.
Lower
2.329
-0.043
-1.831
-6.756
-0.483
Regression Equation Results
Dependent Variable, Y: DefRate%
Indep. X Variables
Intercept
TotalPd'n
NumStaff
Supervisor
MinTemp
R-Squared
Multiple R
Adj. R-Squared
Standard Error of
Estimate
Durbin-Watson
Number of
Observations
Coefficien
t
25.498
-0.001
-0.948
-3.545
0.03
Standard
Error
9.798
0.018
0.373
1.358
0.217
t-Statistic
2.6024
-0.0387
-2.5396
-2.6105
0.1401
95%
Conf.
Upper
48.667
0.042
-0.065
-0.334
0.544
VIF
1.572
1.261
1.487
1.174
75.94%
0.8714
62.19%
1.929
1.998
12
(a) What does the F-ratio, and associated results, tell us?
(b) For the regression printout shown, all four independent variables have been included in the
regression model. Write down the multiple regression equation:
(c) Is there any evidence of multi-collinearity in this model? Explain fully?
MSQ791 Data Analysis For Managers – Sample Exam
Page 20
(d) Interpret each of the coefficients in this equation, from a practical point of view:
(e)
Interpret R2 for this regression equation.
(f)
Which of the four independent variables are significant in this relationship? Justify briefly.
(continued)
MSQ791 Data Analysis For Managers – Sample Exam
(g)
(h)
Page 21
Under the best conditions, namely with 15 staff, total output for the Morning shift should
o
be 380 microprocessors. Assuming an outside temperature of 8 C, what is the expected
defective rate:
(i)
If Smith is the supervisor?
(ii)
If Jones is the supervisor?
What conclusions would you draw about the underlying factors behind the defective rate
in the Morning shift? Write a brief report for management.
END OF SAMPLE EXAMINATION PAPER