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This section must answer to the following specific questions
1. What proportions of the students in your sample are local and what proportion are international?
2. What is the relationship between price and average quantity consumed by students?
3. What are the most popular and least popular soft drinks among students?
4. How loyal are students to their brand? (Do students change their preference when they receive a 25% or 40% discount on their preferred drink?)
5. How does the demand (price-quantity relationship) of international students differ from that of local students?
6. What are the most and least popular drinks among local students? How does this compare with the preferences of the international student?
7. 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.

## Sampling Method

The purpose of this report is to provide a detailed analysis on the survey data based on the beverages consumption between domestic students and international students of USC University to understand the preference of beverages among thousands of students of the university. The analysis is performed after selecting a random sample of 90 students. The consumption of beverages is measured with reference to 375ml cans. In this paper, the most preferred beverages have been chosen for total students and for local and international students separately.

All the given requirements are addressed in the course of this study. The dataset is given in the Excel sheet with 200 responses. The random numbers were already calculated using RAND() function in Excel (Mélard 2014). Firstly, the random sample of size 90 is drawn by doing customised sorting of the random numbers.

The proportions of both local and international students are shown in the tabular form below:

 Proportion of local students 0.911111 Proportion of international students 0.088889

The relationship between the price and the average consumed quantity can be evaluated by the correlation coefficient. It is a statistical measure that helps to find out the degree of strength of relationship between two variables. If the coefficient is positive then it represents that for one unit increase in one variable interprets the increase in another variable (Cohen et al. 2013). On the other hand, if there is negative correlation between two variables then it shows that if one variable increases one unit then the other variable will decrease. The Pearson’s correlation coefficient is calculated for this problem using the inbuilt function CORREL() in MS Excel (Carlberg 2014). Before calculating the correlation coefficient, the dataset is processed. The total consumption is calculated by taking sum of the quantity of the consumptions for Soft drinks, Fruit juice, Tea/coffee, Energy drinks, and other drinks. Then the total price is calculated using the SUMPRODUCT() function for multiplying individual price with the demand and finally for summing them (Bluttman 2013).

The value of the correlation coefficient is 0.093 which shows that the relationship between these two variables is positive but very negligible (Cohen et al. 2013).

The most popular and the least popular soft drinks among students can be calculated by counting the preferences for each of the beverages. “1” denotes the first preference and “5” represents last preference. The values of the counts for both the first and last preferences are calculated in Excel using the COUNTIF() function (Carlberg 2014). Then, these values of the counts are tallied to evaluate the most preferred and the least preferred beverages. The following table shows the count of the preferences. The highest preferences for all the drinks are displayed using the yellow color and the least preferences are shown by blue color for easy checking.

 count of highest preference of soft drinks= 15 count of lowest preference of soft drinks= 13 count of highest preference of Fruit Juice 8 count of lowest preference of Fruit Juice 4 count of highest preference of Tea /coffee 16 count of lowest preference of Tea /coffee 20 count of highest preference of Energy drinks 2 count of lowest preference of Energy drinks 46 count of highest preference of Other 49 count of lowest preference of Other 7

## Proportions of Local and International Students

From the values of most preferred counts, it can be seen that other drinks (milk, water and many more) is the most preferred drinks among the students and the least preferred drinks among students is Energy drinks.

The problem is to find the level of loyalty of the students to their preferred brand. The “Yes” response regarding the change of preference is represented by 1 and the “No” responses are represented by 0. To find out how loyal the students are, it is enough to show the proportion of the counts of “No” responses.

The counts and proportion of “No” responses are shown in the following table:

 Count of "No" when the second preference was cheaper than the most preferred beverage of the students Proportion of "No" when the second preference was cheaper than the most preferred beverage of the students 25% cheaper 69 0.766666667 40% cheaper 43 0.477777778

Thus, it can be concluded that students are loyal with probability 0.7667 when the second preference is 25% cheaper and they are loyal with the probability 0.4778 when the second preference is 40% cheaper.

Response to Question 5.

The problem can be addressed by calculating the z-test to check the difference of demands between the international students and the local students (Bubenik 2015). First, the students are grouped on the basis of international students and the local students. Then, the difference between the means of these two groups and the variances for the values of these two groups are calculated (Davis and Pecar 2013). The purpose of this test is to check whether the mean values differ for the two groups. The null hypothesis is that there is no difference between the mean values of the two groups and the alternative hypothesis is that mean values of these two groups differ. The following table shows the calculation of the z-test (Myers, Well and Lorch 2013). This is a two-tailed test. The z-test is obtained using the Data Analysis Tool Pak in Excel.

 z-Test: Two Sample for Means Demand for local students Mean 98.67073 75 Known Variance 15823 5353.143 Observations 82 8 Hypothesized Mean Difference 23.67 z 2.49E-05 P(Z<=z) one-tail 0.49999 z Critical one-tail 1.644854 P(Z<=z) two-tail 0.99998 z Critical two-tail 1.959964

From the following table, it can be seen that the observed test statistic for the two-tailed test is 0.9998 and the critical value of the test statistic at 5% level of significance is 1.959964. Clearly, absolute value of the observed value of two tailed test < critical value of the test statistic. Therefore, the null hypothesis is accepted and there is no difference between the demand of local and international students (Park 2015). Thus, the demands are same for both the groups.

First, the responses are grouped on the basis of local students and the international students. Then, the preferences are counted for the two groups of students. Finally, the respective proportions are calculated since the number of observations between two groups are not same. The following table shows the proportions of preferences.

 Highest pref. for Soft drinks Lowest pref. for Soft drinks Highest pref. for Fruit juice Lowest pref. for Fruit juice Highest pref. for Tea/coffee Lowest pref. for Tea/coffee Highest pref. for Energy drinks Lowest pref. for Energy drinks Highest pref. for other Lowest pref. for other Local Students 0.170732 0.134146 0.097561 0.04878 0.158537 0.243902 0.02439 0.5 0.54878 0.073171 International Students 0.125 0.25 0 0 0.375 0 0 0.625 0.5 0.125

The following grouped bar chart represents the preferences for the soft drinks.

Figure 1: Group Bar Chart for preference of local & international students

Response to Question 7.

The proportion that the student will choose soft drinks as their first preference is p= 0.166666667. Now, the problem requires finding out the 95% confidence interval of this proportion which can be evaluated using the formula p ± z*Ö(p(1-p)/n) ;

z = confidence coefficient which is 1.96 at 5% level of significance (Lang and Altman 2013), n = sample size (Cumming 2013).

Thus, the lower bound and the upper bound are respectively 0.089670595 and 0.243662738. Therefore the confidence interval is (0.089670595, 0.243662738).

From the above data analysis, it can be concluded that the purpose of this analysis has been well addressed by providing the information about the most preferred beverages and the least preferred beverages among the total students and also among the local and international students.  The analysis also provides analysis on the proportion of preferred soft drinks and its confidence interval that will interpret the proportion value will lie between the two ranges, namely, the lower bound and the upper bound.

References

Bluttman, K., 2013. Excel formulas and functions for dummies. John Wiley & Sons.

Bubenik, P., 2015. Statistical topological data analysis using persistence landscapes. The Journal of Machine Learning Research, 16(1), pp.77-102.

Carlberg, C., 2014. Statistical analysis: microsoft excel 2013. Que Publishing.

Cohen, J., Cohen, P., West, S.G. and Aiken, L.S., 2013. Applied multiple regression/correlation analysis for the behavioral sciences. Routledge.

Cumming, G., 2013. Understanding the new statistics: Effect sizes, confidence intervals, and meta-analysis. Routledge.

Davis, G. and Pecar, B., 2013. Business statistics using Excel. Oxford University Press.

Lang, T.A. and Altman, D.G., 2013. Basic statistical reporting for articles published in biomedical journals: the “Statistical Analyses and Methods in the Published Literature” or the SAMPL Guidelines”. Handbook, European Association of Science Editors, 256, p.256.

Mélard, G., 2014. On the accuracy of statistical procedures in Microsoft Excel 2010. Computational statistics, 29(5), pp.1095-1128.

Myers, J.L., Well, A.D. and Lorch Jr, R.F., 2013. Research design and statistical analysis. Routledge.

Park, H.M., 2015. Hypothesis testing and statistical power of a test.

Cite This Work

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