**Group Assessment – Cover page **

**Cover Page **

**Instructions **

**Group Assignment Questions **

**Question 1 (10 marks) **

Suppose that the average waiting time for a patient at a physician’s office is just over 29 minutes. To address the issue of long patients’, wait times, some physicians’ offices are using wait-tracking systems to notify patients of expected wait times. Patients can adjust their arrival times based on this information and spend less time in waiting rooms. The following data show wait times (in minutes) for a sample of patients at offices that do not have a wait-tracking system and wait times for a sample of patients at offices with such systems. The data are stored in **HI6007 Group Assignment T1 2024 data file (sheet 1). **

a) Calculate the mean and median patient wait times for offices;

i. with a wait-tracking system?

ii. without a wait-tracking system?

**(2 marks) **

b) Calculate the variance and standard deviation of patient wait times for offices; i. with a wait-tracking system?

ii. without a wait-tracking system?

**(2 marks) **

c) Create a box plot for patient wait times for offices;

i. with a wait-tracking system and review the information from the box plot? ii. without a wait-tracking system and review the information from the box plot? **(4 marks) **

d) Do offices with a wait-tracking system have shorter patient wait times than offices without a wait-tracking system? Explain.

**(2 marks)**

**Question 2 (10 marks) **

Suppose a researcher has collected sample data on beer price (in $/per litre) and per capita beer quantity consumed (in litres) in Australia between 1975-2017. The data are stored in **HI6007 Group Assignment T1 2024 data file (sheet 2). **

Answer the following questions

a) Prepare a numerical summary output for the two variables; beer price and per capita beer quantity consumed and explain the key numerical descriptive measures.

**(2 marks) **

b) Based on the numerical descriptive measures, comment on the shape of the distribution of the two variables; beer price and per capita beer quantity consumed.

**(2 marks) **

c) Test the hypothesis that the population mean per capita beer consumption is less than 135 litres/year.

**(2 marks) **

d) If the researcher claims that the population mean per capita beer consumption is greater than 135 litres/year do you agree with that? Explain why.

**(2 marks) **

e) Based on part (c) and (d), what can you say about the population mean per capita beer consumption in Australia?

**(2 marks) **

**Question 3 (20 marks) **

Dixie Showtime Movie Theatres, Inc. owns and operates a chain of cinemas in several markets in the southern United States. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. The data are stored in **HI6007 Group Assignment T1 2024 data file (sheet 3). **Using this data set and EXCEL, and no more than 1500 words in total, answer the following questions.

a) Using an appropriate numerical descriptive measure, comment on the strength and the direction of the linear relationship between weekly gross revenue and television advertising; and weekly gross revenue and newspaper advertising.

**(2 marks) **

b) Develop a simple linear regression model to estimate the relationship between weekly gross revenue and television advertising expenditure and Comment on the goodness of fit of the estimated model.

**(2 marks) **

c) Develop and estimate a multiple linear regression model to estimate the relationship between weekly gross revenue and television and newspaper

advertising expenditure. **(2 marks) **

d) What do the estimated regression coefficients in part (c) reveal about the relationship between weekly gross revenue and television and newspaper advertising expenditure? **(2 marks) **

e) Test the overall validity of the estimated multiple regression model in part (d) at the 5% level of significance.

**(2 marks) **

f) Test whether linear relationship exists between weekly gross revenue and individual independent variables in part (d) at the 5% level of significance.

**(2 marks) **

g) Will your conclusion in part (f) change if the level of significance changes to 1% level of significance?

**(1 mark) **

h) Compare the fitness of the multiple linear regression model with that of the simple linear regression model.

**(2 mark) **

i) Based on your answers to (a) to (h) above, write a research report (of maximum 300 words) for the head of research division of your company, summarizing your findings and highlighting the managerial implications of these results?

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