Statistics for the Behavioral and Social Sciences

Question: Discuss about the Statistics for the Behavioral and Social Sciences. Answer: Introduction 5 years ago, David Geoffs had started a coffee roaster, coffee supplier, and outlet operator that were named as 'Sublime Delight'. David Geoff had turned his passion into profession. 'Sublime Delight' used to produce three main products Espresso Delight,, Mocha Delight, and Sublime Delight. This was done by experimenting on various kinds of beans, their moisture levels and their roasting patterns. David Geoff had begun his business called as micro roasting set-up. He had shipped organically grown coffee beans from Australia and he had stored them under various controlled conditions. The products he created had consistent flavours, their beans were easy to grind, and had a good lifetime. This had helped the shop to offer their customers an identifiable and repeatable coffee product. It had also helped the shop to produce a manageable and cost effective production process. Eighteen months ago, Geoff had decided to branch out his coffee shop into two takeaway or coffee cart operations and three mobile units operations. Here, BADIR methodology was used to investigate the data set to provide information to the board members on few things about their business. The board members wanted to know about the sales and profits were distributed over the outlets and what their major growth areas were. Existence of any difference between the quality of services and quality of coffee across the outlets are also another concern of the board members. Information would also be provided about the validity of the bean-mix supply across different period. Background and content David Geoff had started 'Sublime Delight five years ago by transforming his passion of having superior quality coffee into a profession. Importing organically grown coffee beans from Australia; i.e. from his site, he mixed coffee beans of various qualities to produce varieties of coffee. David Geoff used to preserve the seeds under various conditions and gradually developed three primary products Espresso Delight, Mocha Delight, and Sublime Delight. Branching out into take away and mobile marts eighteen months age, the aim of the assignment is to provide an idea about the distributions, profit, sales and growth of his company across different areas and outlets. The quality of the service and the quality of the coffee would also be dealt with in this assignment and the validity of the prediction about the bean-mix would also be judged. Methodology BADIR Methodology BADIR methodology is an useful process that helps the managers to take their decisions. BADIR methodology has five steps, which involves Business questions, Analysis plan, Data collection, Interpretation and Recommendation. The methodology is given below in the following tasks: Business question How sales and profits are distributed across outlets? Where are the major growth areas? Analysis plan The data would be analysed using various statistical methods to find the solution of the business question. Statistical methods would be used to find the total sale price and profit from the data set. Data collection The data were collected from the months of January and December for External customers, internal carts and mobiles. This collected data was used for to answer the business questions. Investigation The sales were found to be almost evenly distributed in all the given outlets. The amount of sales in all the outlets was in the range of $1038.23 to $1491.574 (Aron et al. 2013). It was seen that the sales across every outlets increased gradually from January to December. The sale was least in January and maximum in the month of December. To find the distribution of profit in the sales: It was seen that the profit for 17 external customers had increased from the month of January till June (Le and Eberly 2016). There was a little decrease in the profit till the month of October. There was an increase in the profit in the month of November. The maximum profit for this variable reached in the month of December. It was seen for the variable the internally owned cart outlets that the profit of this outlet had increased from the month of January to the month of October. There was a decrease in the profit of the sales for this outlet in the months of November and December (Grchenig 2013). The rate of increase of the profit of mobile set ups was slow and it reached the maximum profit in the month of December. External customers were the major growth area for Sublime delight. This is because the rate of growth of the profit was maximum for external customers. It was seen that there was a difference of $1000 in the profit of Sublime Delight between the months of January and December for the external customers (Sharma et al. 2016). It is seen that the percentage of sales in category external customers is 44.43%, the percentage of sales for internal carts is 43.25% while the percentage of sales for mobiles is 12.32 percent. There was difference in sales across the different outlets and the maximum sales was found to be at the outlet external customers. On analysing the distribution of profit across the three outlets, it was seen that external customers had the profit of 43.26%, internal carts had the profit of 48.37% while mobiles had the profit of 8.37%. It was seen that there was internal carts had the maximum profit out of the three outlets of Sublime Delight. This suggests that most of the sales of Sublime Delight lay at internal cart as the profit for this outlet is maximum. The graphs of the sales for three different outlets are given below: Figure 1: Sales in external customers (Source: Created by author) Figure 2: Sales in internal cart (Source: Created by author) Figure 3: Sales in Mobiles (Source: Created by author) The sales show that the sales for every outlet had been increasing from January to December. However, there was a dip in the sale across the three outlets for the month of July and August. It can be interpreted that there is seasonality effect in the sale of the three outlets. Truck location and time is expected to effect the business as longer the time taken to reach the outlets, there would be lesser inventory in the outlets. The trucks are expected to carry the inventories to the outlets and it is expected that the location of truck would affect the business. The basic overall profit differs across the three outlets where mobiles have lesser profit and internal cart have the most profit. Recommendation It is recommended that the company must improve their policies for the month of October as the profit for this month was found to decrease than the other months. Business question Is there any significant difference between the outlets in terms of service quality and coffee quality? Analysis plan The data will be collected for Outlet, Service, Coffee and Frequency. These collected data would be analysed using pivot table and frequency method. Data collection Data was collected for Outlet, Service, Coffee and Frequency. These collected data will be analysed to provide the solution of the business question. Investigation It was seen that there was significant difference across the outlets for the quality of the services and quality of the coffee. This is because the customers gave maximum number of 5 grades to outlet 3. The customers gave minimum number of 5 grades to outlet 1. It can be interpreted that the customers graded outlet 1 as the worst outlet and outlet 3 was graded as the best outlet. This shows that there is significant difference between the services across the outlets. Yes, the variable frequency is categorical data as the data is divided into four groups. The variable is categorised according to the frequency of the purchase from the outlet. The remaining three variables are ordinal variables. The rating of the customers suggests that both the quality of service and the quality of coffee were excellent across the outlets. It is seen that outlet 3 had the best service and outlet 2 had the worst service. It is also seen that outlet 3 have best quality of coffee while outlet 7 have worst quality of coffee according to the ranking given by the respondents. The sampling error of quality of service was found to be 0.117 while the sampling error of quality of coffee was found to be 0.099 (Lopez et al. 2012). It can be interpreted that sampling error of quality of service is more than the sampling error of quality of coffee. Recommendation It is recommended that the management of the company must provide better facilities and improve the condition of other outlets as well. This would also help to improve the business across all the outlets and the customers would provide them with higher grades. Business questions What is the validity of the new proportion of mix provided to the company for their business? Analysis plan Data was collected for the months of January and December for the variables Espresso, Sublime and Mocha. These collected data would be compared with the new mix provided and interpretation would be provided accordingly. Data collection Data would be collected for the variables Espresso, Sublime and Mocha. The value of the variable would be collected for the months of January and December. Interpretation In order to test whether the given proportion holds for some of the outlets in the month of January, hypothesis test is to be performed for the months of January considering the predicted mixture as 30% espresso, 10% mocha and 60% sublime. Chi square test was used for this purpose. The hypothesis of this test is as follows: H0: The predictions regarding the mix proportion do not hold for January H1: The predictions regarding the mix proportion hold for January Chi square statistic came out to be 0.2079101557072, which is greater than 0.05. This suggests that the test is insignificant and the null hypothesis is accepted. It can be interpreted that the predictions regarding the mix proportion do not hold for January. In order to test whether the given proportion holds for some of the outlets in the month of December, hypothesis test is to be performed for the months of December considering the predicted mixture as 30% espresso, 10% mocha and 60% sublime. Chi square test was used for this purpose. The hypothesis of this test is as follows: H0: The predictions regarding the mix proportion do not hold for December H1: The predictions regarding the mix proportion hold for December Chi square test suggests that the p value of the test is 0.0000000003162, which is smaller than 0.05. This leads to the rejection of null hypothesis was the p value of the test is less than the level of significance of the test; i.e. 0.05. Thus, it can be said that the predictions regarding the mix proportion hold for December. The analysis suggested that there was a change in the taste between the months of January and December. It was seen that the proportion of mixture in the months of January did not match the preferred mixture at various outlets (Sathaliyawala et al. 2013). However, the mixtures at different outlets did match the preferred mixture for the months of December (Boashash 2015). Thus, there was a change in the tastes between the months of January and December. According to the data available, it was seen that the new expected market mix that could be suggested is 37% espresso, 28% mocha and 35% sublime. Recommendation It is recommended that the market mix of 37% espresso, 28% mocha and 35% sublime would be the appropriate mix for the betterment of business. Conclusion From the analysis of the given data it was seen that external customers fetched the maximum profit for Sublime Delight. The profit for external customers had increased throughout the years. The different in the profit between the months of January and December was found to be $1000. The service quality and the coffee quality were found to have significant difference across the outlets. According to the grades of the customers, outlet 3 got the best grades and outlet 8 was graded as the worst outlet. The company had suggested a definite proportion of mixture that would be suitable for their business. However, it was seen that the proposed composition of mixture would be true for the month of January and not for the month of December. It is also predicted that the proportion of mixture must be amended to 37% espresso, 28% mocha and 35% sublime for their better business. References Aron, A., Coups, E. and Aron, E.N., 2013.Statistics for The Behavioral and Social Sciences: Pearson New International Edition: A Brief Course. Pearson Higher Ed. Boashash, B., 2015.Time-frequency signal analysis and processing: a comprehensive reference. Academic Press. Grchenig, K., 2013.Foundations of time-frequency analysis. Springer Science Business Media. Le, C. T., and Eberly, L. E. 2016.Introductory biostatistics. John Wiley Sons. Lopez, O., Haboucha, A., Chanteau, B., Chardonnet, C., Amy-Klein, A. and Santarelli, G., 2012. 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