Business Statistics Annual Number of Admissions to the Movies

 

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.

 

 

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 statisticsand your knowledge of multiple linearregression 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:
Variable Definition
Admissions (millions) Ticket admission to movie theatres in millions of customers
Screens Number of theatre screens available in Australia
Theatres Number of theatres open in Australia
Films Screened Number of films screened in Australia
Top Price Top Price of theatre ticket in Australia in 2014 $
Capacity Daily Capacity of customers in 000s.

Required:

A. Calculate the descriptive statistics fromthe data and display in a table. Be sure to comment on the central tendency,variabilityand shape for each variable. (1 Mark)
B. Draw a graph that displays the distribution of admissions. (1 Mark)
C. 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? (1 Mark)
D. What is the likelihood that the admissionsaregreater than 70 millionif the real price of tickets exceeds $20.00?Are admissions statistically independent of price? Use a Contingency Table. (2 Marks)
E. Estimate the 95% confidence interval for the population mean theatre capacity. (1 Mark)
F. 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. (1 Mark)
G. Run a multiple linear regression using the data and show the output from Excel. (1 Mark)
H. 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. (2 Marks)
I. Interpret the remaining slope coefficient estimates.Comment on whether the signs are what you are expecting. (2 Marks)
J. Interpret the value of the Adjusted R2. Is the overall model statistically significant at the 5% level of significance? Use the p-value approach. (1 Mark)
K. 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. (3 Marks)
L. Based on the results of the regressions, is it likely that other factors have influencedthe theatre admissions? If so, provide a couple possible examples and indicate whether these would likely influence the regression results if they were included. (1 Mark)
M. 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)(1 Mark)

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Allocation of Marks:
Professional Business Report 2 Marks
Part A 1 Mark
Part B 1 Mark
Part C 1 Mark
Part D 2 Marks
Part E 1 Mark
Part F 1 Mark
Part G 1 Mark
Part H 2 Marks
Part I 2 Marks
Part J 1 Mark
Part K 3 Marks
Part L 1 Mark
Part M 1 Mark
Total: 20 Marks
Year Admissions (millions) Screens Theatres Films Screened Real Ticket Price Capacity (‘000s)
1994 28.9 822 702 223 19.71 377
1995 29.7 742 573 194 19.82 324
1996 35.5 676 509 239 19.90 295
1997 30.8 645 506 259 19.63 303
1998 37.4 712 520 281 19.66 285
1999 39 772 501 291 19.43 286
2000 43 851 510 252 20.41 295
2001 46.9 885 522 240 19.25 301
2002 47.2 906 510 229 19.39 296
2003 55.5 951 518 259 19.44 300
2004 68.1 1028 537 252 20.76 312
2005 69.9 1137 557 253 20.54 332
2006 73.9 1251 551 281 20.21 356
2007 76 1422 563 285 20.08 387
2008 80 1576 567 273 19.84 413
2009 88 1748 580 255 19.54 446
2010 82.2 1817 554 250 19.38 453
2011 92.5 1855 547 245 19.30 463
2012 92.5 1872 547 258 19.52 464
2013 89.8 1907 553 268 19.56 471
2014 91.5 1909 520 318 20.00 460