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Exam Sample with answers...

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Sample Exam Paper (Guide Only)

 Final exam will consist of 60 Multiple Choice Questions (MCQ).

 Please refer to “How to Fill Multiple Choice Answer Sheets?” (available online).

 Please remember to write your name and student ID at the top of the multiple choice answer sheet with your responses (failing to do so may result in failing the exam).

Problem 1 (Hypothesis testing) A company that manufactures travel goods is particularly concerned that the mean weight of the roll-on cabin bags should not exceed 3 kg as many airlines limit the weight of carry-on luggage on their planes to 5 kg. Past experience allows the assumption that the std. dev = 0.03 kg. A sample of 50 cabin bags is selected and the sample mean is 3.009 kg. Using a 0.05 significance, conduct a hypothesis test to determine if the population mean weight of the cabin bags is greater than 3kg?

What is the null and alternative hypothesis for this test? A

H0: µ ≥ 3, H1: µ < 3

B

H0: µ ≤ 3, H1: µ > 3

C

H0: µ = 3, H1: µ ≠ 3

D

H0: µ ≠ 3, H1: µ = 3

E

None of the above

What is (are) the critical value(s)? A

-1.96 and 1.96

B

-1.645

C

-1.645 and 1.645

D

1.645

E

None of the above

What is the calculated test statistic? A 2.12 B 1.43 C 1.78 D

1.23

E

None of the above

What is your conclusion? (Choose the most correct answer) A Reject Ho at the 5% level of significance. B Accept Ho at the 5% level of significance. C Not sure. D None of the above. E Need more information.

Calculate the p-value A P value = 0.017 B P value = 0.09 C P value = 0.05 D Not sure E None of the above

Interpret the meaning of the p-value

A The probability of observing a test statistic more extreme than the observed sample value given the null hypothesis is true. B The observed level of significance. C The smallest value of α for which H0 can be rejected. D All of the above E None of the above

Problem 2 (Multiple Regression):

A developer who specialises in holiday cottage properties is considering purchasing a large tract of land adjoining a lake. The current owner of the tract has already subdivided the land into separate building lots and has prepared the lots by removing some of the trees. The developer wants to forecast the value of each lot. From previous experience, she knows that the most important factors affecting the price of the lot are size, number of mature trees and distance to the lake. Y: price in thousands of dollars X1: lot size in hundreds of square metres X2: number of mature trees X3: distance to the lake in metres

What is the best interpretation for the estimated coefficient for Trees? A

For every additional tree, the estimated property price does not change

B

For every additional tree, the estimated property price increases by $679

C

For every additional tree, the estimated property price increases by $0.679

D

For every additional tree, the estimated property price decreases by $679

E

None of the above

Does Lot-size have a statistically significant effect on property prices at the 5% level of significance? Why/Why not? A

Yes, as the p-value is less than 0.05

B

No, because the t-stat is too low

C

No, because the p-value is less than 1.96

D

Not enough information

E

None of the above

Interpret the 95% confidence interval associated with the coefficient Trees: A

Irrelevant as the number of mature trees have an insignificant effect on property prices.

B

We are 95% confident that each mature tree will increase property price by $700

C

We are 95% confident that each mature tree will increase property price between $220 and $1138

D

We are 95% confident that each mature tree will increase property price between $600 and $800

E

None of the above

Interpret the R2 A 24% of variation in property prices can be explained by variation in the X variables B 76% of variation in property prices can be explained by variation in the Y variables C 30.94% of variation in property prices can be explained by variation in the X variables D 31.81% of variation in property prices can be explained by variation in the Y variables E None of the above

What is the purpose of the F-test? A

To test the significance of the observations

B

To test the average model fit

C

To test the individual significance of the regressors

D

To test the overall significance of the model

E

None of the above

What is the null and alternative hypothesis in the F-test?

A

H0: β1 = β2 = β3 < 0, H1: At least one βj ≥ 0

B

H0: β1 < β2 < β3 < 0, H1: At least one βj ≥ 0

C

H0: β1 = β2 = β3 = 0, H1: At least one βj ≠ 0

D

H0: β1 ≠ β2 ≠ β3 ≠ β4 ≠ 0, H1: At least one βj = 0

E

None of the above

What are the results of the F-test? A

Lot-size and Distance are insignificant but Trees is statistically significant

B

None of the variables has a significant effect on property prices

C

At least one of the independent variables has a significant effect on property prices

D

Not enough information

E

None of the above

Predict the price of a house with 2 mature trees,2 metres distance to the lake and lot size 600 square metres A

$56.192

B

$56192

C

$78,156

D

$81,853

E

None of the above

Practice Questions Problem 4: A company is having a new corporate website developed. In the final testing phase the download time to open the new home page is recorded for a large number of computers in office and home settings. The average download time for the site is 2.5 seconds. Suppose that the download times for the site are normally distributed with a standard deviation of 0.5 seconds.

a) What is the probability that download time will be less than 2 seconds?

b) What is the probability that a download time is between 1.5 seconds and 2.2 seconds?

c) What is the minimum weekly mean download time for the top 20% of downloads?

Problem 5:

Using quarterly data on the retail turnover in the hospital industry from 1983 to 2007, the following regression was obtained: log( y^ ) = 3.13 + 0.007X -0.036Q1 -0.0398Q2 -0.03Q3 Where: y denotes the retail turnover in the hospitality industry x denotes the time trend where X = 1 for the first quarter in 1983 Q1 is set to 1 for quarter 1 and 0 otherwise Q2 is set to 1 for quarter 2 and 0 otherwise Q3 is set to 1 for quarter 3 and 0 otherwise Using the above information answer the following questions: a) What is the value of the Y-intercept?

b) How would you interpret this value (the Y-intercept)? c) Unadjusted forecast for the retail turnover in the first quarter of 1983

d) What is the estimated quarterly compound growth rate? e) What is the value of the first quarter multiplier?

f) What is the value of the third quarter multiplier?

g) How would you interpret this value? h) What is the forecast for Quarter 1, 2008 (Hint: X1 = 101)?

5) The following table lists the average price and quantity consumed for a selection of food products.

Kiwi fruit Rockmelon Watermelon

2000 2.60 1.80 0.35

Price (per kg) 2005 3.10 1.90 0.39

2010 3.38 2.15 0.44

2000 5.2 21.6 24.8

Quantity (kg) 2005 5.5 19.8 25.9

What is the unweighted aggregate price index in 2005 using 2000 as the base year? A B C D E

106.02 67.59 113.5 335.02 None of the above

What is the best interpretation for this? A B C D E

The overall price rise from 2000 to 2005 was 6.02% The overall price rise from 2000 to 2005 was 13.5% The overall price rise from 2000 to 2005 was 47.95% The overall price rise from 2000 to 2005 was 235.02% None of the above

What is the Paasche price index in 2005 using 2000 as the base year?

2010 4.9 20.5 26.3

A B C D E

approximately 163.12 approximately 165.29 approximately 147.95 approximately 169.55 None of the above

What is the Paasche price index in 2010 using 2000 as the base year? A B C D E

335.02 343.34 323.15 None of the above

What is the best interpretation for this? A B C D E

X

The overall price rise from 2000 to 2010 was 223.15% The overall price rise from 2000 to 2010 was 243.34% The overall price rise from 2000 to 2010 was % The overall price rise from 2000 to 2010 was 235.02% None of the above

Singapore apartment prices

Melbourne apartment

prices Mean Standard Error Median Mode Standard Deviation Sample Variance Range Minimum Maximum Q1 Q3

355 5 351 382 25 621 106 292 398 341 381

483 28 549 N/A 148 21911 543 270 813 430 682

What is the coefficient of variation of the Singapore apartment prices? What is the coefficient of variation of the Melbourne apartment prices? What can be concluded by comparing these statistics? A B C E

Singapore apartment prices experience higher relative variability than Melbourne apartment prices. Melbourne apartment prices experience higher relative variability than Singapore apartment prices Melbourne and Singapore apartment prices share the same relative variability None of the above

Question 5 What is the Interquartile Range of the Singapore and Melbourne apartment prices respectively?...