2020 mock fit1006 PDF

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Page 1 of 12

Instructions

Mock Exam: DO NOT "SUBMIT". Doing so will close off your access to the sample exam. We do not have the ability to reopen the mock exam once it has been submitted.

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Essay Questions The number of Kit Kats and Mars Bars sold over 11 days at a milk bar are given below. Observation A

B

C

D

E

F

G

H

I

J

K

Kit Kats (y) 20

9

6

10

5

0

9

6

5

10

5

Mars Bars (x)

5

6

8

9

10

11

12

13

14

16

1

6

(a) Calculate the q-correlation of the data. (3 marks) (b) Comment on any unusual observations, that is, those that would significantly affect the least squares regression equation of y on x. Describe their effect. Note: You are not required to calculate the least squares regression equation. (3 marks)

(a) Exponentially smooth the following time series using alpha = 0.5. Include the forecast value for the 4

time series in Period 6. (2 marks)

Period

1

2

3

4

5

6

Value

20

20

24

16

21

xxx

Smoothed

(b) If the observed value in period 6 is 25, what is the MAPE of the forecast values? (2 marks)

The prices of certain commodities and the quantities consumed per month are given for the years 2009 and 2019. Calculate the Fisher Price Index for the given data. (2 marks)

2

Item Quantity 2009 Quantity 2019 Price 2009 Price 2019 A

40

30

$6.00

$10.00

B

50

35

$8.00

$13.00

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The following extracts show the CPI, All Groups, published by the ABS, December Quarter 2015 and 2

December Quarter 2012. Using this information, if petrol cost, on average, $1.30 per litre in Melbourne in 2014 - 15, what should it have cost in 2008 - 09? (2 marks)

Explain the main differences between probability and non-probability designs for sampling. Briefly 4

mention the advantages and disadvantages of each, giving at least one reason why a person may choose a non-probability survey design. Give two examples of each type of design. (4 marks)

A book publisher expects to find one flaw in every 8 pages of printing. A new book requires 72 pages to be printed. (4 marks)

4

(a) What is the probability that the printing will contain no flaws? (b) What is the probability that the printing will contain more than 5 flaws?

The number of cameras sold each week by a retailer is recorded for a small sample of shops as: 20, 15, 18, 11, 18, 16 10. Calculate a 99% confidence interval for the average number of cameras sold each week. (4 marks)

4

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In a survey of 1000 voters, 530 indicated that they would vote for the Coalition in the coming election. On the basis of these data test the hypothesis that the Coalition will win the election, which requires a

5

simple majority. (Assume a 99% confidence level). (5 marks)

Gas consumption for a particular customer has been recorded over two years. Each year has 6 billing seasons. The table shows actual consumption, seasonal indices and deseasonalised consumption. Period (X)

Consumption Billing Season

Index

mj

8

Deseasonalized (Y)

1

18.94

1

0.40

47.18

2

32.95

2

0.66

50.25

3

90.70

3

2.00

45.40

4

90.40

4

1.97

45.95

5

35.33

5

0.71

49.88

6

12.02

6

0.23

51.19

7

19.92

1

0.40

49.63

8

31.28

2

0.66

47.69

9

99.13

3

2.00

49.61

10

95.78

4

1.97

48.68

11

31.47

5

0.71

44.44

12

10.12

6

0.23

43.11

Summary Stats: ΣX = 78.00

ΣY = 573.0

ΣX2 = 650.0 ΣY2 = 27433.8 ΣXY = 3692.6

(a) Calculate the least squares equation predicting deseasonalised consumption for each period. (2 marks) (b) Using the regression equation calculated in part (a), calculate deseasonalised consumption for periods 15 and 16. (2 marks) (c) Using your results from part (b) forecast actual consumption for periods 15 and 16. (2 marks) (d) What proportion of the variance in deseasonalised consumption is explained by the regression equation? (r2). (2 marks)

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Estimate the correlation coefficient (to the nearest 0.1) from the scatterplots below.(2 marks) (a)

2

(b)

The following summary statistics were obtained from survey data: = 100,  = 73,  =16. (a) Test the hypothesis that the data come from a population having a mean of 70, against the one-

10

sided alternative that the mean is greater than this. Assume a 1% significance. (4 marks) (b) What is the power of the test if the true population mean is 73? (4 marks) (c) What is the p-value of the hypothesis test? (Hint: 0:  = 70,  = 100,  = 73,  = 16) (2 marks)

The number of withdrawals made annually by account holders is to be analysed by a credit union. Construct a stem and leaf plot and briefly discuss the data. Note: You are not expected to calculate the

4

mean or standard deviation however you may use descriptive statistics to describe the data. (4 marks) 16

7

20

24

4

60

3

16

6

50

11

2

0

21

2

26

10

47

2

3

65

8

32

27

19

4

17

An investment in building an office tower has the following payoff ($m). (4 marks) Payoff($m)

-100

0

10

100

Probability

0.1

0.2

0.3

0.4

4

(a) Calculate the mean and standard deviation of the investment’s payoff. (b) If the project cost $35m to build state with reasons whether you consider the project to be a good or bad investment.

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In Melbourne, we expect it will rain one day in a fortnight on average. Melbourne weather forecasters correctly predict fine weather 85% of the time and correctly predict rain 75% of the time. (2 marks)

2

(a) What is the probability that the weather forecasters will forecast rain? (b) What is the probability that it will rain when the forecasters have predicted rain?

A gambler plays a game where they guess the outcome of a coin toss by predicting “Heads” or “Tails” when the coin is thrown into the air.

5

(a) If a game consists of 50 coin tosses write down the name and parameters of the exact distribution for the number of guesses the player gets correct. (2 marks) (b) Using a Normal approximation, calculate the probability that the player gets 22 or fewer guesses correct. (3 marks)

Student #12345 obtained the following summary statistics for their assignment data using SYSTAT. Recall that the data gives the one-year return on an investment of $1000. Comment on the main

4

features of the data. State with reasons the investment option (1 – 6) you consider to be the best. State also with reasons, the investment you consider to be the worst. (4 marks) Investment Option

1

2

3

4

5

6

N of Cases

70

96

96

16

90

109

Minimum

397.6

300.4

83.0

1150.7 1123.4

897.5

Maximum

13308.6 1741.5 6287.6 1256.4 1643.6 2158.4

Arithmetic Mean

1846.4 1181.1 1218.7 1188.7 1230.0 1210.6

Standard Deviation 1402.2

116.1

608.4

34.6

71.8

107.2

1.00%

570.8

589.6

343.6

5.00%

1540.7 1133.1 1074.9 1151.5 1140.3 1141.2

95.00%

1866.1 1270.2 1301.6 1255.9 1326.7 1293.0

99.00%

11034.5 1544.0 5179.0 1256.4 1575.0 1727.8

Q1

1649.9 1163.7 1119.2 1163.4 1186.6 1173.6

Q2

1705.0 1179.0 1149.2 1181.0 1217.8 1198.3

Q3

1743.3 1203.0 1181.4 1200.9 1263.0 1226.1

1150.7 1127.1 1000.3

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