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:

Question 1  

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:

ii. Ordinal variable:

iii. Discrete variable:

iv. Continuous variable:

v. Dummy variable:

Question 4  

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. 

Question 5  

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:

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?

ii. What is the probability that a person is not Very Aware of Climate Change?

iii. What is the probability that a person is Female and Very Aware of Climate Change?

iv. What is the probability that a person is Female or Very Aware of Climate Change?

v. What is the probability that a person is Very Aware of Climate Change, given that the person is Female?

Question 6  

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?

Question 7  

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? 

Question 8  

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?

Question 9  

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.

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.

ii. Provide a plain language interpretation of the interval you constructed in part i.

iii. The Energy Council of Australia (ECA) have calculated the current 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 currently pay on average? Explain your reasoning.