The assignment must be provided in the form of a (brief) business report approximately 7-10 pages (including this cover page). You must submit an electronic copy of your assignment in Blackboard. Hard copies will not be accepted. SHOW YOUR WORK for Calculation based questions if you wish to receive partial credit.
This assignment requires the use of Microsoft Excel. If you have Windows, you will also need to use the Data Analysis ToolPak. If you have a Mac with Excel 2011, you will need to use StatPlus:MAC LE.
Group Members:
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First name
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Last name
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Student ID
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Please indicate your tutor and tutorial time:
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Tutor
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Tutorial date and time
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Problem Description:
The following data correspond to the annual number of admissions (in millions) to the movies in Australia over the years 1994 and 2014. It also contains the yearly totas of the number of screens, theatres and flims screened, as well as the top price paid for a cinema ticket.
You will use descriptive statistics, inferential statistics and your knowledge of multiple linear regression to complete this task.
Admissions (Dependent Variable) and several characteristics (Independent Variables) are given in the Excel file: Tuesday.xlsx.
Here is a table describing the variables in the data set:
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Variable
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Definition
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Admissions (millions)
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Ticket admission to movie theatres in millions of customers
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Screens
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Number of theatre screens available in Australia
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Theatres
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Number of theatres open in Australia
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Films Screened
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Number of films screened in Australia
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Top Price
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Top Price of theatre ticket in Australia in 2014 $
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Capacity
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Daily Capacity of customers in 000s.
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Required:
- Calculate the descriptive statistics from the data and display in a table. Be sure to comment on the central tendency, variability and shape for each variable.
- Draw a graph that displays the distribution of admissions.
- Create a box-and-whisker plot for the distribution of the top price and describe the shape. Is there evidence of outliers in the data?
- What is the likelihood that the admissions are greater than 70 million if the real price of tickets exceeds $20.00? Are admissions statistically independent of price? Use a Contingency Table.
- Estimate the 95% confidence interval for the population mean theatre capacity.
- Your supervisor recently stated that theatre admissions from 2008 through 2014 (ie. last 8 years) have exceeded the admissions in Taiwan which have been a constant 84 million per year. Test her claim at the 5% level of significance.
- Run a multiple linear regression using the data and show the output from Excel.
- Is the coefficient estimate for the real ticket price in 2014 $ different than zero at the 5% level of significance? Set-up the correct hypothesis test using the results found in the table in Part (G) using both the critical value and p-value approach. Interpret the coefficient estimate of the slope.
- Interpret the remaining slope coefficient estimates. Comment on whether the signs are what you are expecting.
- Interpret the value of the Adjusted R2. Is the overall model statistically significant at the 5% level of significance? Use the p-value approach.
- Do the results suggest that the data satisfy the assumptions of a linear regression: Linearity, Normality of the Errors, and Homoscedasticity of Errors? Show using scatter diagrams, normal probability plots and/or histograms and Explain.
- Based on the results of the regressions, is it likely that other factors have influenced the theatre admissions? If so, provide a couple possible examples and indicate whether these would likely influence the regression results if they were included.
- If a community housing organisation asked for information regarding the characteristics of housing targeting the households of native born Australians, explain whether a simple random sampling technique would provide an accurate representation of these households. (Note: This question does not use the data) (Assume the sampling was conduced across the city).