The aim of this report if to provide the results of the analysis of the data on the consumption of movies across various States in the United States.In the report will provide mathematical as well as visual analyses of the random sample obtained from a population of consumers from several states.The methodology of the study is based on quantitative analysis which majors on the statistical interpretations to obtain insights which can be used to make generalisations about the population data.The data used for the analysis was downloaded from the Canvas and is presented in the Appendix section of the report.
Analysis
Selection of a random sample
Simple random sampling is a technique in which all the population data have an equal chance of being selected into the sample.One of the ways of selecting the sample is to randomly choose 50 numbers between 1 and 4815 and use them to represent the customer number, afterwards the numbers can be used to extract the details of the customers from the population.
Also, we can use excel to generate 50 random numbers between 1 and 4815 and thereafter use the numbers as customer number. The number can afterwards be used to extract consumer details from the population data.
Descriptive Statistics
City
The city of phoenix recorded the highest number of movies purchased with an average of 38 purchases per client, this list was joined by the city of San Francisco and Tampa which all recorded over 30 purchases on average. On the other hand, the quantity of purchase was minimal in the city of Indianapolis which only recorded an average purchase of 17 movies.
The table below summarises the average purchases made by each city
State
When looking at the average dollar amount which was spent in each state for the movie downloads, the state of Phoenix led with an average of $ 241 per client, San Francisco, and Tampa were among the top three states with highest consumer spending with the clients spending an average of over $ 190 on each state.
The movie average expenditure was lower in the state of Indianapolis which recorded an average spending of below $ 130.Below is a tabular summary of average expenditure per state
Between the male consumers and the female ones, more purchases were made by the male compared to their female counterparts. This difference though was slightly small with the male making an average purchase of 24.64 compared to the 23.88 of the females.
The pie chart below summarises the average purchases by each gender
First choice
From the movie categories that the consumers rated as their first choices, SciFi recorded the highest average purchases at 29.87 while Action was the most unpopular with only 19.06 of average purchases.
From the table below its apparent that the most preferred type of movies by the client is the SciFi followed closely by the comedy movies.
Second choice
Among the consumers second choice movie selection Action was the most downloaded with an average of 32.20 purchases by each client. Drama followed closely with 30.50. under this category of choice Comedy was the most unpopular with only an average of purchase of 19.53 for each client. The figure below gives a visual illustration of this.
Age
The average age of the movie clients stands at 45.44 years, this fluctuates by 16.47 years. From all the state the oldest client was 70 years while the youngest was 15 years old.
Purchases
The average number of purchases from all the cites stands at 24.26 per consumer, this fluctuated by 10.41 to maximise at 44 while minimising at 8.
Dollar amount
Averagely each consumer spent 156.98 dollars on the movies. At the minimum a consumer spent $ 53 on a movie while the highest spent by a client was $ 277.
More details regarding the age, purchases and the dollar amount statistical analysis is availed in the appendix
Confidence interval
We are 95% confidence that the average number of purchases for first choice SciFi movies is 29.87. Also, we are 95% confidence that the average dollar amount spent by a consumer to purchase the movies is 156.98.
The mean of the sampled population at 95% confidence interval is lower than the true mean which is obtained as 32.58 purchases per client. Furthermore, the true average dollar amount spent by each client to purchase movies for the entire population stands at 166.71 which is higher than the 156.98 obtained for the sampled population.
The calculations are shown in the appendix
Hypothesis testing
To verify the notion that the average amount spent for the first-choice comedy movies is higher than the average amount spent on the drama movies, a statistical test was carried out. From the result obtained it can be concluded that sufficient evidence was obtained from the sample data to conclude that the mean amount spent on the first-choice comedy is not greater than the average spent in the first-choice drama movies.
Also, from the mathematical calculations it was evidence that the sampled data contains enough evidence to conclude that; the average quantity of purchases by the males and the females do not differ.The statistical tests calculated were done with a confidence of 95%. This indicates that the results obtained have a 5% chance of being inaccurate.
The details and results of the statistical tests are available in the appendix.
Correlation and regression
Age and dollar amount
The statistical model developed to study the relationship between the age and the dollar amount spent on the movies indicates that there is no significance relationship between the two variables. Only 0.98% of the changes can be stated to be explained by the change in the age. Farther analysis provides sufficient evidence to allow a statistical conclusion that the coefficient of the independent variable on the linear model is 0. This goes on to add to the proof that the two variables have no statistical significance relationship, it is thus not practical to use the age of the clients to predict their expenditure on the movies.
Purchase and dollar amount
The study of the relationship between the amount of purchases and the dollar amount spent indicate that the model developed to study the two is statistically relevant.
Farther analysis indicate that the coefficient of the independent variable is not zero which proves that there is a correlation between the two and one can be used to assist predict the other.The scatterplot below explains this relationship In the graph the dollar amounts is represented by y while the variable x represents the purchases.
From this we can deduce the linear relationship
As the relationship between the two variables.
The value of R is obtained as 0.9888, this indicates that there is a very strong correlation between, the volume of purchases and the total amount of expenditure in dollars.In addition, the R squared is given as 0.9777, an indication that 97.77% of the changes in the amount spent is due to the changes in the quantities being purchased by the consumers.
The equation obtained have a slope of 6.4554. This value means that should the quantity being purchased increase by a single unit, the amount of dollar being spent will increase by 6.4545. Also, the equation has an intercept of 0.3721, this signals that when the unit of purchases is zero the consumers are only spending $ 0.3721. This can be speculated to be other costs (such as internet search for the movies) which are independent of the volume of movies purchased.
Conclusion
The data analysis used a quantitative approach, this applies statistical and mathematical calculations to interpret the sampled data, afterwards the obtained information is used to generalise the entire population.
The descriptive analysis indicated that the city of Phoenix had the highest average movie purchase per client with Indianapolis experiencing the lowest average quantity of movies purchased. When it comes to the average expenditure spent by a client on the movies, consumers from the state of phoenix had the highest value with an average expenditure of $ 241. The state of Indianapolis recorded the minimum movie expenditure per client.
Generally, males purchase more movies compared to their female counterparts though this difference is small.Out of the consumers first choice movie types, SciFi recorded the highest average purchase by clients. Also, out of the second-choice movie types, actions were the most popular with the highest average purchases by consumers.
The statistical tests conducted to tests the notions highlighted by the research indicated that, the average amount spent on first choice drama movies is not higher than the average amount spent on the first-choice drama movies. Furthermore, there is no evidence to support the theory that the average quantity purchased by the males and the females do differ.
The study of correlation indicates that the age of the consumers has no significance relationship on the amount spent on the movies. The case is however different when the quantities purchased are compared to the amount spent, up to 97.77% of the changes in the dollar amount spent in the movies is due to the differences in the quantities purchased by the clients.One of the limitations of the research is the small sample size that may not represent the overall population efficiently.
References
Andrew, G., 2008. Variance, analysis of. The new Palgrave dictionary of economics. 2nd ed. Basingstoke, Hampshire New York: Palgrave Macmillan.
Bailey, R. A., 2008. Design of Comparative Experiments, s.l.: Cambridge University Press.
Klaus, H. & & Oscar, K., 2008). . Design and Analysis of Experiments. I and II ed. s.l.:Wiley.
Scott, J. A., 2012. Illusions in Regression Analysis. International Journal of Forecasting, 28(3), p. 689.
Willem, W., Baets, D. & Luc, B., 2008. ROC analysis in ordinal regression learning. Pattern Recognition Letters, Volume 29, p. 1–9.
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