Preliminary Comment for Section 1 (Question 1 to Question 4)
The Australian Government has developed a survey to enable it to gauge the views of the Australian public regarding “Climate Change”. The survey consists of a sample of 400 Australian Citizens and Permanent Residents regarding their views on a wide range of Climate Change topics.
The Government intends to use the results of the survey to assist in the formulation of government policy for the next 30 years.
The variables used in the dataset are as follows:
Variable Name
Explanation
Options
Monthly_Payment
Amount willing to pay monthly ($) in order to have net zero electricity bills through renewable energy (e.g. Solar panels with battery)
Up_Front_Payment
Amount willing to pay up front ($) in order to have net zero electricity bills through renewable energy (e.g. Solar panels with battery)
Age
Your Age in Years
Gende
Gender you most identify with
{Male, Female}
Income
Your income in Dollars
State
State in which you normally reside
{NSW, Vic, Qld, WA, SA, Tas, ACT, NT}
Locality
If you live in a city or the country
{U
an, Rural}
Education
The highest level of Education achieved
{Pre High School, High School, TAFE Certificate, Bachelor Degree, Postgrad Degree, PhD}
Politics
Which political party you most associate yourself with
{Coalition, Labour, Green, Minor Parties}
Support
Belief that Australia should financially support developing countries in their efforts to address Climate Change
{Yes, No}
Govt_Policy
How happy you are with the Australian Government's cu
ent policies on Climate Change
{Very Dissatisfied, Dissatisfied, Unsure/Unfamiliar, Satisfied, Very Satisfied}
Lead Role
Who should take the most responsibility in addressing Climate Change
{Australian government, State governments, Local government, Industry/Companies, Individuals/Families}
Cause
Who/what you think is most responsible for Climate Change
{Mostly Human, Mostly Natural, There is no Climate Change, Unsure/Undecided}
Awareness
Awareness you have regarding Climate Change
{Very Aware, Moderately Aware, Have a little knowledge, Have no Interest/Awareness}
Affected
The extent you believe you have been affected by Climate Change
{Severely affected, Somewhat affected, Not affected}
Seriousness
Seriousness of Climate Change on Australian society (1 - Not Serious, 10 - Extremely Serious)
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Concerned
Your concern with cu
ent situation regarding Climate Change
{Not concerned, Slightly concerned, Somewhat concerned, Very concerned, Extremely concerned}
Solar_Panels
Willingness to Install Solar Panels
{Already Installed, Plan to Install, Would Install if I could, No plan to install/Do not want}
Energy_Source
Which Energy Source you believe should be Australia's largest contributor to national Electricity generation
{Solar, Hydro, Wind, Coal, Gas, Oil, Nuclear, Other Renewable}
News_Source
Your prefe
ed News Source to learn about Climate Change
{Internet, Newspapers, Magazines, Research Journals, TV, Social Media, Other}
Question 1 (5 points)
Read the Preliminary Comment carefully and then answer the following questions.
For each of the variable types below, identify and write one matching variable name from the table above. If there are no matching variable names, then write “Nil”.
i. Nominal variable: [1 mark]
ii. Ordinal variable: [1 mark]
iii. Discrete variable: [1 mark]
iv. Continuous variable: [1 mark]
v. Dummy variable: [1 mark]
Question 4 (5 points)
The Government also wants the sample size to be large enough so that they can be 95% confident that the amount of money (in $) the Australian Public are prepared to pay Up Front for 100% renewable energy is within $110. A pilot survey was undertaken previously and the standard deviation was found to be $650. Show your workings. [5 marks.]
Question 5 (10 points)
The Government wants to know whether there is a relationship between people having an Awareness of Climate Change and Gender. Results from the survey are shown in the cross-tabulation below:
Awareness
Total
Very Aware
Moderately Aware
Little Awareness
No Awareness
Gende
Male
64
44
39
41
188
Female
88
64
41
19
212
Total
152
108
80
60
400
From the above table, answer the following probability questions, assuming that we randomly select a person from the 400 people in the sample:
i. What is the probability that a person is Very Aware of Climate Change? [2 marks]
ii. What is the probability that a person is not Very Aware of Climate Change? [2 marks]
iii. What is the probability that a person is Female and Very Aware of Climate Change? [2 marks]
iv. What is the probability that a person is Female or Very Aware of Climate Change? [2 marks]
v. What is the probability that a person is Very Aware of Climate Change, given that the person is Female? [2 marks]
Question 5 options:
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Question 6 (2 points)
A report published in one of the national newspapers recently suggests that 30% of people in Australia have Little or No Awareness of Climate Change.
What is the probability that of 20 residents selected at random, 10 or more had Little or No Awareness of Climate Change? [2 marks]
Question 7 (2 points)
Based on previous studies, Australian residents change their electricity supplier on average three times every 10 years.
What is the probability that a randomly chosen resident in Australia will change their electricity supplier more than five times in a given 10 year period? [2 marks]
Question 8 (5 points)
It is believed that the annual amount spent by households on electricity bills in Australia follows a Normal distribution with a mean (µ) of $1900 and a standard deviation (σ) of $350.
What is the probability that a randomly selected household in Australia will be paying less than $1200 annually? [5 marks.]
Question 9 (10 points)
The following summary measures describe the monthly amount Australians are willing to pay in order to have completely renewable energy as their electricity supply. This information has been gathered from the sample of 400 Australian residents.
Monthly_Payment ($)
Mean
145
Standard E
o
16
Median
80
Mode
0
Standard Deviation
161
Sample Variance
25921
Kurtosis
5.46
Skewness
1.21
Range
500
Minimum
0
Maximum
500
Sum
58000
Count
400
Complete the following tasks using the above summary measures.
i. Construct a 99% confidence interval of the Monthly_Payment amount Australians would be prepared to pay for electricity that was sourced form a totally renewable energy source. (Show your workings) [5 marks]
ii. Provide a plain language interpretation of the interval you constructed in part i. [3 marks]
iii. The Energy Council of Australia (ECA) have calculated the cu
ent average monthly electricity bill in Australia at $130. Is there any evidence to suggest that the amount Australians are willing to pay in order to have completely renewable energy as their electricity supply is more than the amount they cu
ently pay on average? Explain your reasoning. [2 marks]
Question 9 options:
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Question 10 (9 points)
Of the 400 customers who were randomly surveyed, 108 believed that Climate Change was not a problem.
i. Calculate a 95% confidence interval for the true proportion of all Australians that believe that Climate Change is not a problem. (Show your workings) [4 marks]
ii. Provide a plain language interpretation of the interval you constructed in part i. [3 marks]
iii. In part i, we have used a confidence level of 95%. What does the confidence level mean? Do we always use 95%? Explain. [2 marks]
Question 11 (4 points)
The Australian Government is interested in the proportion of people who are either Satisfied or Very Satisfied with cu
ent Government Climate Change policies. They believe that they have the support of the majority of Australians.
You are to conduct a hypothesis test to check their Claim. The random sample of 400 customers shows that 225 people were either Satisfied or Very Satisfied with the cu
ent Government policies.
Write down the Null and Alternative hypotheses in both Symbols and Words for the above situation. [4 marks.]
Question 11 options:
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Question 12 (4 points)
For the Hypothesis Test above, use a level of significance (α) of 5% when answering the following questions.
i. What is the critical value(s)? [2 marks]
ii. State your decision rule? [2 marks]
Question 12 options:
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Question 13 (4 points)
For the Hypothesis Test above, calculate the value of the test statistic. [4 marks]
Question 13 options:
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Question 14 (3 points)
For the Hypothesis Test above, state your decision then, in plain language, your conclusion. Explain your reasoning. [3 marks.]
Question 14 options:
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Question 15 (2 points)
Based on your answer to Question 14, would the p-value be less than 5%? Explain why/why not. [2 marks.]
Question 15 options:
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Question 16 (3 points)
With hypothesis testing, there is always the risk that you will reach an inco
ect conclusion. Based on your answer to Question 14, what type of e
or (Type I or Type 2 e
or) could be made here? Explain what this means in the context of the Australian Government’s claim. [3 marks]
Question 17 (3 points)
The dataset was analysed using the co
elation and regression analysis routines of Excel to develop a multiple regression model for the variable Monthly_Amount* with the independent variables Age, Gender (Female = 1, Male = 0) and Salary (in $).
* Monthly_Amount is the amount a person is willing to pay in order to have net zero electricity bills through renewable energy (e.g. Solar panels with battery)
Excel’s regression output is reproduced below.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.8241
R Square
0.6791
Adjusted R Square
0.6767
Standard E
or
XXXXXXXXXX
Observations
400
ANOVA
df
SS
MS
F
Significance F
Regression
3
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
0.0000
Residual
396
XXXXXXXXXX
XXXXXXXXXX
Total
399
XXXXXXXXXX
Coefficients
Standard E
o
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
91.3564
35.5927
2.5667
0.0106
21.3820
XXXXXXXXXX
21.3820
XXXXXXXXXX
Age
-2.0757
0.7979
-2.6014
0.0096
-3.6443
-0.5070
-3.6443
-0.5070
Gender (F=1, M=0)
5.6544
17.8697
0.3164
0.7518
XXXXXXXXXX
40.7857
XXXXXXXXXX
40.7857
Salary
0.0024
0.0002
28.7764
0.0000
0.0021
0.0027
0.0021
0.0027
State how well this model explains the variation in Monthly_Payment? [3 marks.]
Question 17 options:
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Question 18 (11 points)
Using the Regression model above:
i. Write down the regression equation [2 marks.]
ii. Using the regression equation from part i. predict the value of Monthly_Payment (in $) if the person was 45 years of age, Female, and had a Salary of $90,000. [3 marks.]
iii. Interpret the coefficient for “Gender” from a practical point of view. [3 marks.]
iv. Identify if any of the three independent variables in the model are insignificant at the 5% level of significance? Explain your reasoning. [3 marks.]
Question 19 (5 points)
The following graphs marked A, B, C and D are of four different time series.
For each of the five questions listed below, select just one time series graph from above (by letter) which is the best example of its type, or is the most appropriate model. If none are appropriate, select the letter X.
i. Exhibits a weak linear trend component: