Question 10  

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.

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

iii. In part i, we have used a confidence level of 95%. What does the confidence level mean? Do we always use 95%? Explain.

Question 11  

The Australian Government is interested in the proportion of people who are either Satisfied or Very Satisfied with current 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 current Government policies.

Write down the Null and Alternative hypotheses in both Symbols and Words for the above situation.

Question 12  

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)?

ii. State your decision rule?

Question 13  

For the Hypothesis Test above, calculate the value of the test statistic.

Question 14  

For the Hypothesis Test above, state your decision then, in plain language, your conclusion. Explain your reasoning.

Question 15  

Based on your answer to Question 14, would the p-value be less than 5%? Explain why/why not. 

Question 16  

With hypothesis testing, there is always the risk that you will reach an incorrect conclusion. Based on your answer to Question 14, what type of error (Type I or Type 2 error) could be made here? Explain what this means in the context of the Australian Government’s claim.

Question 17  

The dataset was analysed using the correlation 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

State how well this model explains the variation in Monthly_Payment?

Question 18  

Using the Regression model above:

i. Write down the regression equation

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.

iii. Interpret the coefficient for “Gender” from a practical point of view.

iv. Identify if any of the three independent variables in the model are insignificant at the 5% level of significance? Explain your reasoning.]

Question 19  

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: A  B  C  D  X

ii. A regular cycle is apparent: A  B  C  D  X

iii. Little or no correlation with time: A  B  C  D  X

iv. An exponential trend model fits the data: A  B  C  D  X

v. A strong linear trend model fits the data: A  B  C  D  X

Question 20

The following tables consists of Prices and Consumption for three types of energy products in Australia for 2007 and 2017 

a. Using 2007 as the base year, calculate the Laspeyres aggregate price index.

b. Interpret the Laspeyres price index.