tptm6495 s1 2012 - practice exam answers

BUSINESS SCHOOL

TPTM6495Analysis Tools for Transport and LogisticsSemester One, 2012

Practice Exam Answers (30%) Time: 2 hours

This exam is worth 30 percent of your final grade. You have two hours to complete the exam. Once you enter the room you will not be allowed to leave until the end of the exam unless accompanied by a supervisor.

Instructions

1. This exam comprises of a total of 17 pages.

2. For this exam you may bring:a. A double sided piece of A4 paper.b. Writing implements.c. A nonprogrammable calculator (helpful).

3. No other items will be allowed in the room.

4. Ensure that your mobile phone is switched off and is not on your desk.

5. Only answers completed in this booklet will be marked.

6. The exam is out of 100. 20 multiple choice questions worth two marks each (40 marks in total) and 3 short answer questions worth 20 marks each (60 marks in total).

The multiple choice questions will be marked according to the following framework:

Two marks for a correct answer. Zero marks for a blank answer. You will lose a mark for a question that you answer but get incorrect.

Failure to comply with these instructions will result in a mark of zero being recorded.

PRACTICE EXAM

Section A.Multiple Choice Questions (20 questions worth 2 marks each).

Circle the correct answer.

1. What is a type I error?

a. Not rejecting the null when the null is falseb. Rejecting the null when the null is falsec. Rejecting the null when the null is trued. Not rejecting the alternative when the alternative is false e. None of the above

2. A real estate agent sells a house for $520,000, but on average houses, in the area sell for $845,000 with a standard deviation of $220,000. What is the standardised (Z) score for the sale price of the house?

a. 1.877b. 1.477c. -1.877d. -1.477e. None of the above

3. For children between the ages of 18 months and 29 months, there is approximately a linear relationship between “height” and “age”. The relationship can be represented by: Y = 64.93 + 0.63(x), where Y represents height (in centimetres) and X represents age (in months). Joseph is 22.5 months old and is 80 centimetres tall. What is Joseph’s residual?

a. 79.1b. -0.9c. +0.9d. 56.6e. 64.93

4. For children, there is approximately a linear relationship between “height” and “age”. One child was measured monthly. Her height was 75 cm at 3 years of age and 85 cm when she was measured 18 months later. A line was fit to her data. The slope of this line is approximately:

a. 0.55 cm/monthb. 10 cm/monthc. 25 cm/monthd. 1.57 cm/monthe. 2.1 cm/month

5. Preference for mode of transport (where commuters are required to place car, bus and train in order of most preferred to least preferred) is an example of what kind of data?

a. Nominalb. Normalc. Ratiod. Ordinale. Interval

PRACTICE EXAM6. There is an approximate linear relationship between the height of females and their age

(from 5 to 18 years) described by:

height = 50.3 + 6.01(age)

Where height is measured in cm and age in years. Which of the following is not correct?

a. The estimated height of a child who is 10 years old is about 110 cm.b. The estimated intercept is 50.3 cm which implies that children reach this height

when they are 50.3/6.01=8.4 years old.c. The average height of children when they are 5 years old is about 50% of the

average height when they are 18 years old.d. My niece is about 8 years old and is about 115 cm tall. She is taller than average.e. On average, children between 5 and 18 grow 6.01 cm per year.

7. In hypothesis test, the null hypothesis is:

a. Always false.b. A change from the accepted state.c. Never accepted.d. Results in something dying.e. Defines the current state of nature.

8. What is the standard deviation for the following number range?

4 41 11 17 7 47 10 16 17 32 36

a. 14.6b. 14.8c. 10.8d. 11.1e. None of the above

9. Which of the following are properties of ratio data?

a. Additiveb. Divisablec. Fixed zero pointd. All of the abovee. None of the above

10. Boxplots are useful in identifying?

a. Intervalsb. Mediansc. Homoskedasticityd. Multicolinearitye. None of the above

PRACTICE EXAM11. Elasticities can be calculated by using what model form?

a. Multiplicative modelb. Exponential modelc. Quadratic modeld. All of the abovee. None of the above

12. Where will the maximum value of the object function occur for the following linear programming model, if the objective function is P = 5x + 7y?

a. Point Ab. Point Bc. Point Cd. Point De. Point E

13. A problem has 3 decision variables and 5 constraints. How many basic variables are used to solve this problem?

a. 3b. 5c. 8d. 2e. None of the above

14. Linear programming operates under deterministic assumptions. What does this mean?

a. Values of outputs are known with certainty. b. Values of inputs are known with certainty.c. Values of inputs are unknown.d. Values of outputs are unknown.e. Values represent a unique solution.

15. The correct correlation statistic for non-normal data is what?

a. Pearsonb. Spearmanc. R-squaredd. Chi-squarede. None of the above

PRACTICE EXAM16. Data analysis is the process of:

a. Running statistical modelsb. Making recommendationsc. Answering questionsd. Creating a set of facts with meaninge. Making educated guesses

17. Which of the following is not affected by outliers:

a. Meanb. Modec. Standard Deviationd. All of the abovee. None of the above

18. If 65% of the data is plus or minus one standard deviation, the data has what sort of distribution?

a. Normalb. Poissonc. Binomiald. Exponentiale. Not enough information to tell

19. Consider the following crosstab (with a Chi-Square of 12.831, sig. = 0.005) where the researcher looked at the amount of speed at which a package is delivered using various methods.

Bike Car TruckQuick 57% 75% 50%Slow 43% 25% 50%

Which of the below statements is most correct?

a. There is no significant relationship between delivery speed and delivery modeb. There is a significant relationship between delivery speed and carc. There is a significant relationship and using a car provides quick delivery speedd. There is a significant relationship and quick delivery speed result in a car being usede. There is a significant relationship, but there is no difference between truck and bike

20. Which of the following is not an assumption of regression analysis?

a. Normality of the errorb. Constant variancec. Linearityd. Normality of the dependent variablee. All of the above

- THIS IS THE FINAL QUESTION FOR SECTION A -

PRACTICE EXAM

Section B.

Short Answer Questions (3 questions worth 20 marks each).

Answer in the space provided

Question 1

a. What is aggregation bias? Give your own example of when this might be a problem. (4 marks)

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b. What is the problem with extrapolation in regression analysis? (4 marks)

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PRACTICE EXAMc. What is homoskedasticity? (4 marks)

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d. How would you test for multicollinearity? (4 marks)

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e. How does dummy coding affect the regression equation? Give an example of this. (4 marks)

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PRACTICE EXAM....................................................................................................................................

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THIS IS ADDITIONAL WRITING SPACE FOR QUESTION 1:

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Question 2

The Sydney Symphony Orchestra has asked you to examine some of the inventory process that the organisation uses when dealing with the programs for selected musical performances. For the orchestra, the sale of concert programs constitutes a large part of concert revenue and is critical to the profitability of the Symphony.

PRACTICE EXAM

As a consultant examining this situation you have collected the following information:

Number of Programs Number of TimesSold (in 100's) Sale Level Achieved

23 18

24 24

25 30

26 42

27 6

Based on interviews, Sydney Symphony has never sold any less than 2,300 programs or more than 2,700 programs. Each program costs $0.80 to produce and they sell for $3.00. Any programs that are not sold are recycled and do not produce any revenue.

a. Explain what technique you would use to examine this problem and why. (6 marks)

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b. If the orchestra decided to print 2,500 programs for each performance, what would be the average profits over 10 performances? (5 marks)

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PRACTICE EXAM....................................................................................................................................

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....................................................................................................................................c. If the orchestra decided to print 2,600 programs for each performance, what would be the

average profits over 10 performances? (5 marks)

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PRACTICE EXAM....................................................................................................................................

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d. How might you improve this analysis and how would you suggestions make it better? (4 marks)

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PRACTICE EXAMQuestion 3

a. Interpret all components of the following sensitivity output (10 marks)

Adjustable Cells

Name Final ValueReduced

CostObjective

CoefficientAllowable Increase

Allowable Decrease

Litres Produced (Red Wine) 200 0 700 50 10Litres Produced (White Wine) 150 0 400 15 20

Constraints

Name Final ValueShadow

PriceConstraint R.H. Side

Allowable Increase

Allowable Decrease

Bottling Used 200 100 200 25 25Working Hours Used 3640 50 3640 70 100

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....................................................................................................................................b. The Traffic Bureau have studied the number of accidents at an intersection, and following is

output from a regression model:

PRACTICE EXAM Y = Number of Accidents

Numped = Number of pedestrians at crossing

Numcars = Number of cars at intersection

Speedlim = Speed limit at intersection

Weather 0=dry, 1=wet

Lightcol = Colour of light (1=red, 2=yellow, 3=green)

Model Summaryb

.994a .987 .984 20.60740Model1

R R SquareAdjustedR Square

Std. Error ofthe Estimate

Predictors: (Constant), numped, numcars, weather,lightcol, speedlim

a.

Dependent Variable: numaccb.

ANOVAb

614901.3 5 122980.252 289.594 .000a

8068.630 19 424.665622969.9 24

RegressionResidualTotal

Model1

Sum ofSquares df Mean Square F Sig.

Predictors: (Constant), numped, numcars, weather, lightcol, speedlima.

Dependent Variable: numaccb.

Coefficientsa

-360.292 29.232 -12.325 .000.929 .331 .084 2.802 .011 .768 1.303

8.088 .882 1.014 9.174 .000 .056 17.935-12.357 17.513 -.064 -.706 .489 .083 12.01846.665 9.504 .145 4.910 .000 .784 1.2762.312 1.519 .086 1.522 .144 .214 4.670

(Constant)numcarsspeedlimlightcolweathernumped

Model1

B Std. Error

UnstandardizedCoefficients

Beta

StandardizedCoefficients

t Sig. Tolerance VIFCollinearity Statistics

Dependent Variable: numacca.

PRACTICE EXAM

20-2

Regression Standardized Residual

8

6

4

2

0

Freq

uenc

y

Mean =-3.49E-15Std. Dev. =0.89

N =25

Histogram

Dependent Variable: numacc

1.00.80.60.40.20.0

Observed Cum Prob

1.0

0.8

0.6

0.4

0.2

0.0

Expe

cted

Cum

Pro

b

Normal P-P Plot of Regression Standardized Residual


20-2

Regression Standardized Predicted Value

1.5

1.0

0.5

0.0

-0.5

-1.0

-1.5

-2.0Reg

ress

ion

Stan

dard

ized

R

esid

ual

Scatterplot


numpedweatherlightcolspeedlimnumcars

num

ped

wea

ther

light

col

spee

dlim

num

cars

a. What might be wrong (if anything) with the model above? (6 marks)

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PRACTICE EXAM....................................................................................................................................

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b. Interpret the adjusted R-square. (2 marks)

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c. Which variable has the biggest impact on the number of traffic accidents? Why? (2 marks)

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- THIS IS YOUR FINAL QUESTION-

PRACTICE EXAMAdditional Space

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tptm6495 s1 2012 - practice exam answers

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