Data Analysis

This section must answer to the following specific questions

- What proportions of the students in your sample are local and what proportion are international?

- What is the relationship between price and average quantity consumed by students?
- What are the most popular and least popular soft drinks among students?
- How loyal are students to their brand? (Do students change their preference when they receive a 25% or 40% discount on their preferred drink?)

- How does the demand (price-quantity relationship) of international students differ from that of local students?

- What are the most and least popular drinks among local students? How does this compare with the preferences of the international student?
- How likely is it that the student will choose soft drink (Pepsi, Coke etc.) as their first preference? Provide 95% confident interval estimates and interpret your results.

USC university is attended by thousands of students in a day with varying preferences to drinks. The objective of the assignment is to understand the student’s drinks market in the university. To achieve the objective, BAC21 students were interviewed and the data recorded. A sample of 100 responses was generated from the sample selected and used for analysis so as to; know the proportion of international and local students in the university, know general and specific relationship between price and demand for various drinks for the different categories of students, understand the loyalty of students to their preferred drinks and know the probability that student chose soft drink as their first preference.

To collect the sample from the data recorded in spreadsheet, random numbers were generated using the “RAND ()” function and stored in column A of the sheet (Levie, 2008). Thereafter, the data was sorted from largest to smallest on the basis of the random numbers generated, and the first one hundred samples were taken as the preferred sample and stored in sheet two of the spreadsheet. Analysis was done on the basis of the sample generated.

Data Analysis

The sample of one hundred students generated had a proportion of local students equal to 0.9 (90%) and a proportion of international students equal to 0.1 (10%) as depicted in the figure below. The proportion is given by count of individual category divided by the total of both categories (Shao, 2010).

A pie chart was used as a graphical representation of the proportions of the local and international students (Rumsey, 2007). It is as shown below:

To determine the relationship between price and average quantity consumed by the students, the sum for demand in for each price category of demand was determined and used to plot a scatter diagram (Bruce, 2015). The scatter diagram was fitted with a line of fit and the regression equation to draw a general conclusion of the relationship between the variables (Hinton, 2014). The scatter plot is as shown below:

It is evident that there is a strong negative linear relationship between price and the demand. As the price of any drink goes up, the demand goes down and vice-versa.

The most and least popular drinks among the students are determined based on the consumption of each type of drink by the student. The table below represents the drinks in their order of their consumption.

A bar chart is used to the graphically indicate the consumption of different categories of drinks.

It is noted that other drinks such as water and milks drinks have the highest demand among the students hence are the most popular. On the other hand, energy drinks have the least demand among the students and hence are the least popular.

The loyalty of students to their brand is based upon the whether they can or cannot change their preference when they receive a 25% or 40% discount on their preferred drinks. From the table below, a proportion of 26% of the students would change their preference given 25% discount while a proportion of 74% would not change. Likewise, a proportion of 58% would change their preference when given a 40% discount for the second preference while 42% would no change. In general terms, a small discount such as 25% would only cause a small proportion to shift their preferences while a bigger proportion would not change. However, an increase in discount to 40% would result to majority of students changing their preference as opposed to those who would not change.

## Summary

The pie charts below represent the proportions of students who would change or not change their preferences given 25% and 40% discount respectively.

To determine how the demand for international students differed from that of local students, we first determined the mean demand for each category of students (Lock et al, 2013). The mean was used because it’s the measure of central location that indicates where the distribution of demand for each category of students would be centered (Croucher, 2016). The table below summarizes the demands of each category of students and the means.

A bar-chart is drawn to graphical represent the variation of mean demand of local and international students. It is as shown below.

From the table above, it can be generalized that the demand of each category increases with decrease in price. However, local students have generally more average demand compared to international students as indicated in the bar-chart.

The table below shows the most popular to the least popular drinks among the local and the international students. The columns for proportion are used instead of the total consumption for each category in making the final conclusion so that it can be representative of all members of the populations (Evans and Basu, 2013).

The distribution of the drinks consumption for the various categories of students graphically represented in the chart below:

It is evident that other drinks such as water and milk drinks are the most popular soft drink among the local students and international students. However, more local students prefer this drinks compared to international students. The least popular drink among the international and local students is the energy drink. However, more international students consume the energy drinks compared to the local students.

The likely hood of students choosing soft drink (Pepsi, Coke etc.) as their first preference is determined as probility of the Z-score in the standard normal table (Rugg and Petre, 2007). The mean of consumption is 709.6, the standard deviation is 847.6823, the value of soft-drinks is 391 the z-score is given by:

The probability from standard normal table 0.352. Therefore, the probability a student choosing soft drink is 0.352. The 95% confidence interval is determined using the formula below (Foster, Barkus and Yavorsky, 2006)

E is the mean error given by:

Where is the critical value of z for 95% confidence interval which is 1.96 (Freund, 2014).

The confidence interval is therefore;

The confidence interval means that there is 95% possibility that the limits 543.45 to 875.75 contain the average number of drinks consumed by the students (Linoff, 2008).

Summary

Analysis of the sample data indicates that the university’s greatest proportion consists of local’s as compared to international students. Both local and international students have individual preferences to drinks. Other drinks such as water and milk drinks are the most popular type of drink for both categories of students. The least popular drink for both categories is the energy drink. Moreover, it is evident that the demand of drinks increase with decrease in price with the mean demand of local students being greater than that of international students. The proportion of student who would change their preference as a result of a discount for the second preference increases with increase in the discount offered. There is a probability of 0.325 that a student would choose soft drink as his first preference and at 95% confidence interval the limits contain the mean amount of drinks consumed by the students. The sample collected is large enough relative to the population under consideration and therefore can be taken as a true representation of the whole population.

References

Bruce, P. 2015. Introductory statistics and analytics. 2^{nd} ed. New Jersey: Wiley.

Croucher, J. S. 2016. Introductory mathematics & statistics. 6^{th} ed. Australia: North Ryde, N.S.W. McGraw-Hill Education.

Evans, J. R., and Basu, A. 2013. Statistics, data analysis, and decision modeling. 5^{th} ed. Boston: Pearson.

Foster, J. J., Barkus, E., and Yavorsky, C. 2006. Understanding and using advanced statistics. 2^{nd} ed. London: SAGE.

Freund, J. E. 2014. Modern elementary statistics. 12^{th} ed. Boston: Pearson.

Hinton, P. R. 2014. Statistics explained. 3^{rd} ed. London: Routledge, Taylor & Francis Group.

Levie, R. D. 2008. Advanced Excel for scientific data analysis. 2^{nd} ed. New York, NY: Oxford University Press.

Linoff, G. 2008. Data analysis using SQL and Excel. 2^{nd} ed. Indianapolis, Ind.: Wiley Pub.

Lock, R., Lock, P., Morgan, K., Lock, E. and Lock, D. 2013. Statistics: Unlocking the power of data. 1^{st} ed. Hoboken, N.J.: Wiley.

Rugg, G., andPetre, M. 2007. A gentle guide to research methods. Maidenhead: Open University Press.

Rumsey, D. (2007). Intermediate statistics for dummies. 1^{st} ed. Hoboken, N.J.: Wiley.

Shao, J. 2010. Mathematical statistics. 2^{nd} ed. New York: Springer.

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