Statistical Analysis Of Admission To Movies In Australia

Methodology

Write an essay on Statistical Analysis.

In this assignment, the “number of admissions” to the movies in Australia was surveyed from the year 1994 to 2014. Other factors were also surveyed in this assignment. The data for the variables of “Screens”, “Theatres”, “Films Screened”, “Real Ticket Price” and “Capacity” were also collected from the year 1994 to 2014 (Bickel and Lehmann 2012). These data were used in this assignment for the analysis.

Statistical analysis would be done on this data set. “Descriptive statistics”, “inferential statistics” and concepts of “linear regression methods” would be given in this assignment based on these data (Vogt and Barta 2013). Graphs and charts would also represent the data and provide conclusion about the data and their relations. 

1. The descriptive statistics for the variables are given below:

Screens
Mean Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper	1213.52381
Standard Error	103.6609083
Median	1028
Mode	#N/A
Standard Deviation	475.0339587
Sample Variance	225657.2619
Kurtosis	-1.569616636
Skewness	0.410014464
Range	1264
Minimum	645
Maximum	1909
Sum	25484
Count	21
Largest(1)	1909
Smallest(1)	645
Confidence Level (95.0%)	216.2328649

Admissions (millions)
Mean	61.82380952
Standard Error	5.151804606
Median	68.1
Mode	92.5
Standard Deviation	23.60853457
Sample Variance	557.3629048
Kurtosis	-1.666346431
Skewness	-0.055528974
Range	63.6
Minimum	28.9
Maximum	92.5
Sum	1298.3
Count	21
Largest(1)	92.5
Smallest(1)	28.9
Confidence Level (95.0%)	10.74647607

Theatres
Mean	545.0952381
Standard Error	9.45840638
Median	547
Mode	520
Standard Deviation	43.34386319
Sample Variance	1878.690476
Kurtosis	8.375821966
Skewness	2.445313468
Range	201
Minimum	501
Maximum	702
Sum	11447
Count	21
Largest(1)	702
Smallest(1)	501
Confidence Level (95.0%)	19.72988992

Films Screened
Mean	257.3809524
Standard Error	5.769573802
Median	255
Mode	259
Standard Deviation	26.43950868
Sample Variance	699.047619
Kurtosis	1.256326286
Skewness	-0.057083837
Range	124
Minimum	194
Maximum	318
Sum	5405
Count	21
Largest(1)	318
Smallest(1)	194
Confidence Level (95.0%)	12.03512002

Real Ticket Price
Mean	19.77952381
Standard Error	0.091997609
Median	19.66
Mode	#N/A
Standard Deviation	0.421586008
Sample Variance	0.177734762
Kurtosis	0.085043332
Skewness	0.91600328
Range	1.51
Minimum	19.25
Maximum	20.76
Sum	415.37
Count	21
Largest(1)	20.76
Smallest(1)	19.25
Confidence Level (95.0%)	0.191903649

Capacity (‘000s)
Mean	362.8095238
Standard Error	15.57082422
Median	332
Mode	295
Standard Deviation	71.35448062
Sample Variance	5091.461905
Kurtosis	-1.582996919
Skewness	0.44357307
Range	186
Minimum	285
Maximum	471
Sum	7619
Count	21
Largest(1)	471
Smallest(1)	285
Confidence Level (95.0%)	32.48017007

Considering the variable “admission (millions)”, the central tendency the variable, i.e. the mean is 61.8238. The median of the variable is 68.1. This is the middle value of the “admission (millions)” is 68.1. The modal value of the variable was 92.5 (Plonsky 2015). This is the maximum frequency for the number of people who were admitted for the movie. The variability of the variable; i.e. the standard deviation is 23.6085. This depicts that the variable had a moderate amount of variability in the “admission (millions)” over the years (Vogt and Barta 2013). The shape of the distribution is “platykurtic” and the distribution is negatively skewed.

The mean of the variable “screens” was found to be 1213.5238. The median of the variable was 1028 and there was no mode for this variable. The standard deviation of the variable was 475.0339 (Thiem 2014). This depicts that there was moderate variation in the number of screens available in Australia for screening of movies. The shape of the distribution id platykurtic and it is positively skewed.

The average value of “theatres” was found to be 545.095. The median of the variable is 547 and its mode is 520. The standard deviation was 43.34. There was a low deviation in the number of theatres open in Australia during 1994 to 2014 (Campbell and Knapp 2013). The shape of the distribution is leptokurtic and the distribution is positively skewed.

The average value of the variable “films screened” was found to be 257.38. The median value was 255 and the modal value was 259 (Ang and Van 2015). The standard deviation was found to be 36.439. This variable had a low deviation of the number of theatres opened in these years. The shape of the distribution is leptokurtic and it is negatively skewed.

Admission

The mean of the variable “real ticket price” is 19.779 and its median is 19.66. the standard deviation of the variable is 0.42 (Kleinbaum et al. 2013). This is a very low standard deviation and the price of the tickets fluctuated little during the period of 1994 to 2014. The shape of the distribution is leptokurtic and the distribution is positively skewed.

The average value of the variable “capacity” was found to be 362.8095. The median was 332 and the mode was 295. The standard deviation of the variable was 71.3544. This depicts that there was moderate variation among the daily capacity of the customers over the years. The shape of the distribution is platykurtic and the distribution is positively skewed.

Graph displaying the distribution of “admission”

Box-and-whisker plot for the distribution of the “real ticket price” is given below

The likelihood that the admission is greater than 70 million when the real price of the ticket is more than $20 is given by P(X > Z) = 1 – P( X< Z) = 1- 0.613 = 0.387 (Campbell and Knapp 2013).

The “admissions” are statistically independent of “price”. This is because the value of the chi square test was found to be zero. The contingency table is as follows:

Sum of probability of admission	Column Labels
Row Labels	28.9	29.7	30.8	35.5	37.4	39	43	46.9	47.2	55.5	68.1	69.9	73.9	76	80	82.2	88	89.8	91.5	92.5	Grand Total
19.25-19.35								0.036												0.071	0.107
19.35-19.45						0.030			0.036	0.043						0.063					0.172
19.45-19.55																	0.068			0.071	0.139
19.55-19.65			0.024															0.069			0.093
19.65-19.75	0.022				0.029																0.051
19.75-19.85		0.023													0.062						0.084
19.85-19.95				0.027																	0.027
19.95-20.05																			0.070		0.070
20.05-20.15														0.059							0.059
20.15-20.25													0.057								0.057
20.35-20.45							0.033														0.033
20.45-20.55												0.054									0.054
20.75-20.85											0.052										0.052
Grand Total	0.022	0.023	0.024	0.027	0.029	0.030	0.033	0.036	0.036	0.043	0.052	0.054	0.057	0.059	0.062	0.063	0.068	0.069	0.070	0.142	1

1. The 95% confidence interval of “mean theatre capacity” is given by (mean – 1.96* s.d.), (mean + 1.96* s.d.) = (460.1412662, 630.0492099)
2. At 5% “level of significance”, the admission from 2008 to 2014 had exceeded the constant amount of 84 millions in Taiwan had the hypothesis as follows:

H₀ = the admission from 2008 to 2014 did not exceed the constant amount of 84 millions in Taiwan

H₁ = the admission from 2008 to 2014 had exceeded the constant amount of 84 millions in Taiwan

On testing the two variables, the p value of the one-tailed test was found to be 0.02732, which is less than the p value (Levy and Lemeshow 2013). The “null hypothesis” in this case is rejected and the admission from 2008 to 2014 had exceeded the constant amount of 84 millions in Taiwan.

1. The output of multiple linear regression is given in sheet named “regression” in the excel file.
2. Using the result of regression analysis, the hypothesis is as follows:

H₀ = there is no difference between the ticket price in 2014 and zero at 5% level of significance

H₁ = there is difference between the ticket price in 2014 and zero at 5% level of significance

The p value of the regression analysis for the variable “real ticket price” had the value of 0.044, which is less than 0.05. This leads to the rejection of “null hypothesis”. Thus, there is difference between the ticket price in 2014 and zero at 5% level of significance. The slope of the variable is 5.2766, which is positive (Montgomery et al. 2015). This states that the variable effects the “admission” in a positive way. The change in price in the ticket leads to the change in the admission in the similar direction.

Screens

The value of intercept was found to be negative. This suggests that the “admission” would be negative in absence of all the factors. The slope of “Screens” was 0.0878, which was slightly positive (Draper and Smith 2014). This value aims to influence the “admission” in a positive manner, as the value is positive. The value of the slope of “Theatres” was found to be 0.04508, which is positive. This depicts that the factor had a weak positive influence of the “admission”. The slope of “Flimsy screened” was 0.001 and it is weakly negative (Csikszentmihalyi and Larson 2014). This also influences the “admission” positively and the change in value of this variable changes the value of “admission” in the same direction (Kleinbaum et al. 2013). The slope of “capacity (‘000s) has a negative slope of -0.2819. This indicates that the variable influence the “admission” in a negative way. The increase in capacity decreases the “admission”.

All the slope of the variables had the same sign as was expected. The sign of “capacity (‘000s)” was expected to be positive whereas it turned out to be negative.

The value of adjusted r square is 0.971. This indicates that 97.1% of variation is explained by only the independent variables that actually affect the dependent variable (Fox 2015).

The p value of the variables “theatres” and “film screened” are more than 5% “level of significance”. The other three variables have their p value less than 0.05. Thus, this overall model is statistically not significant as the p values of all the variables are not less than 0.05.

Scatter diagram and histogram

The variable is heteroscadastic, normal and linear.

Variables like “location of the theatre”, “facilities provided in the theatre” and “the type of movie” influence the “admission” positively. These factors would increase the value of regression coefficient and would thereby, influence the regression coefficient.

The sampling process of random sampling would not be appropriate one at the first instance. The organisation must identify all the households of native-born Australians. They could then use the process of random sampling to select the households from the identified households. 

Conclusion

It was seen from the analysis that the variable “admission” is influenced by various factors like the “Screens”, “Theatres”, “Films Screened”, “Real Ticket Price” and “Capacity”. The “average”, “standard deviation” and the type of distribution of each variable vary from each other over the period from 1994 to 2014. The graphs show the distribution of each variable and the tables give an idea about the type of “admission” with the “real ticket price”. The degree of association between the variables was also analysed. Thus the analysis gave a clear picture about the variables and the effect of “admission” over the years 1994 to 2014 and the influence of the other factors on the “admission”. 

References  

Ang, S. and Van Dyne, L., 2015. Handbook of cultural intelligence. Routledge.

Bickel, P.J. and Lehmann, E.L., 2012. Descriptive statistics for nonparametric models I. Introduction. In Selected Works of EL Lehmann (pp. 465-471). Springer US.

Campbell, J.P. and Knapp, D.J. eds., 2013. Exploring the limits in personnel selection and classification. Psychology Press.

Csikszentmihalyi, M. and Larson, R., 2014. Validity and reliability of the experience-sampling method. In Flow and the Foundations of Positive Psychology (pp. 35-54). Springer Netherlands.

Draper, N.R. and Smith, H., 2014. Applied regression analysis. John Wiley & Sons.

Fox, J., 2015. Applied regression analysis and generalized linear models. Sage Publications

Kleinbaum, D., Kupper, L., Nizam, A. and Rosenberg, E., 2013. Applied regression analysis and other multivariable methods. Nelson Education.

Levy, P.S. and Lemeshow, S., 2013. Sampling of populations: methods and applications. John Wiley & Sons.

Montgomery, D.C., Peck, E.A. and Vining, G.G., 2015. Introduction to linear regression analysis. John Wiley & Sons.

Plonsky, L., 2015. Statistical power, p values, descriptive statistics, and effect sizes: A” back-to-basics” approach to advancing quantitative methods in L2 research.

Thiem, A., 2014. Membership function sensitivity of descriptive statistics in fuzzy-set relations. International Journal of Social Research Methodology,17(6), pp.625-642.

Vogt, A. and Barta, J., 2013. The making of tests for index numbers: Mathematical methods of descriptive statistics. Springer Science & Business Media.