International Journal Mathematics Statistics-Myassignmenthelp.Com

Question: Discuss About The International Journal Mathematics Statistics? Answer: Introducation It is always a desire of each and every organization to maximize on their profits and that is the key reasons as to why they are in business. This is the case of a young upcoming start up by the name Good Harvest. The start-up deals in organic farming and as well as sale of their products direct to their customers. The CEO is concerned about the cost of goods incurred by the start up as well as the sale performance and revenues generated by the enterprise. Business analytics can be used to give clear insights on how the enterprise is performing and probably advise on key areas of improvement. Using the one-year data for the company, we sought to present the CEO with the key analysis related to key areas mentioned. Problem definition and business intelligence required Good Harvest has not been to the market for so long; actually they have been barely two years. The CEO of the company would want to improve the performance of the company but he has to do it through key data insights gained from analyzing the one year that is available. However, the CEO has pointed six key research questions he would want to see answered in the report. His main concern is to understand; What are the worst and top selling products? Do payment methods have variation in terms of total cash received? Do location of the product in the shop have impact on total sales generated? How do sales performance compare for the different months in a year? How do profits of the company compare for the different months in a year? How do sales performance compare for the four seasons? What are the worst and top selling products in terms of sales? Descriptive analysis was used to answer the question. We present two tables; table 1 is for the top selling products while table 2 is for the worst selling products. Table 1: Top selling products Product Class N Minimum Maximum Mean Std. Deviation Water 12 15 6500 1866.88 2541.63 Fruit 54 3 17276 1048.68 2469.41 Vegetable 76 4 5554 871.49 1226.30 Dairy 66 10 10814 619.05 1473.79 Drinks 59 5 11910 574.25 1729.24 Coconut Water 11 21 1794 514.23 562.67 Table 2: Worst selling products Product Class N Minimum Maximum Mean Std. Deviation Stocks Sauces 6 20 49 32.29 12.17 Salad Greens 1 25 25 24.50 Snacks 2 20 21 20.33 0.74 Spices 14 4 129 18.99 32.06 Herbal Teas 4 2 54 17.96 24.37 Juicing 1 5 5 5.00 Six product class had average sales amounting to over $500; these products are categorised under the top selling products. They include; drinks, water, fruit, dairy products, vegetables and coconut water. The bottom six products in terms sales performance include stock sauces, salad greens, spices, juicing products, snacks and herbal teas. The mentioned products have average sales that are less than $50. Is there a difference in payments methods? Organizations do accept different payment methods. There are those which have also restricted payments from some payment methods. Apparently Good Harvest accepts cash payments, credit payments, Visa Card payments as well as MasterCard payments. It would be to the interest of the CEO to understand if there is any of the listed payment methods that brings collects more cash than the other. That is, the CEO would be interested to know whether there is significant difference in the total cash received from the four mentioned payment methods. We the four methods into two categories. One group comprised of cash and credit while the other comprised of Visa Card and MasterCard. Two hypothesis were then tested. Hypothesis 1: H0: There is no significant difference in the total cash received between the cash and the credit payment methods H0: There is significant difference in the total cash received between the cash and the credit payment methods An independent t-test was used for this since cash and credit payments are independent of one another. Independent t-test is used to compare the means of two unrelated groups just like in this case. Table 3: t-Test: Two-Sample Assuming Equal Variances Cash Credit Mean 412.18 604.64 Variance 20811.55 42140.48 Observations 359 354 Pooled Variance 31401.02 Hypothesized Mean Difference 0 df 711 t Stat -14.5002 P(T=t) one-tail 0.000 t Critical one-tail 1.647 P(T=t) two-tail 0.000 t Critical two-tail 1.96 From table 3 above, the p-value was found to be 0.000; this value is less than 5% level of significance hence we reject the null hypothesis and conclude that there is significant difference in the total cash received between the cash and the credit payment methods. In fact, it can clearly be seen that a lot of cash was obtained from the credit payment method as compared to the cash payment method. Hypothesis 2: H0: There is no significant difference in the total cash received between the Visa and the MasterCard payment methods H0: There is significant difference in the total cash received between the Visa and the MasterCard payment methods. An independent t-test was used for this since cash and credit payments are independent of one another. Independent t-test is used to compare the means of two unrelated groups just like in this case. Table 4: t-Test: Two-Sample Assuming Equal Variances Visa MasterCard Mean 576.31 152.55 Variance 50355.11 12000.98 Observations 353 53 Pooled Variance 45418.44 Hypothesized Mean Difference 0 df 404 t Stat 13.49813 P(T=t) one-tail 0.000 t Critical one-tail 1.65 P(T=t) two-tail 0.000 t Critical two-tail 1.965853 From table 4 above, the p-value was found to be 0.000; this value is less than 5% level of significance hence we reject the null hypothesis and conclude that there is significant difference in the total cash received from MasterCard and that received from the Visa Card. In fact, it can clearly be seen that a lot of cash was obtained from the credit payment method as compared to the cash payment method. How does location of the product in the shop affect the sales performance? The hypothesis tested for this question is given below; Hypothesis 4: H0: There is no significant difference in the mean total sales between the different product locations in the shop H0: There is significant difference in the mean total sales between the different product locations in the shop. Analysis of variance (ANOVA) was used to test this hypothesis. ANOVA is applied where we have more than 2 factors to be compared. We had five factors to be compared hence ANOVA was ideal test to be used. ANOVA results are presented in table 5 below; Table 5: Analysis of variance (ANOVA) for the total sales versus product location Total Sales ($) Sum of Squares df Mean Square F Sig. Between Groups 134299725.02 4 33574931.256 37.176 .000 Within Groups 929333380.82 1029 903142.255 Total 1063633105.84 1033 From the ANOVA table above, it is evident that the null hypothesis is rejected (p-value 0.05) and as such we come to a conclusion that the total sales differs depending on the location of the product in the shop. How does sakes compare based on the different months of the year? We tested this using ANOVA where the factors were the months and the net sales was the dependent variable. The hypothesis tested is given below; Hypothesis 5: H0: There is no significant difference in the mean total sales between the different months of the year. H0: There is significant difference in the mean total sales between the different months of the year. Analysis of variance (ANOVA) was used to test this hypothesis. ANOVA is applied where we have more than 2 factors to be compared. We had twelve factors to be compared hence ANOVA was ideal test to be used. ANOVA results are presented in table 6 below; Table 6: Analysis of variance (ANOVA) for the net sales versus months Net_Sales Sum of Squares df Mean Square F Sig. Between Groups 1399993.23 11 127272.11 1.303 .221 Within Groups 34584296.36 354 97695.75 Total 35984289.58 365 From the ANOVA table above, it is evident that the null hypothesis is not rejected (p-value 0.05) and as such we come to a conclusion that the net sales does not significantly differ depending on the month of the year. How does gross profits compare based on the different months of the year? Hypothesis 6: H0: There is no significant difference in the mean gross profits between the different months of the year. H0: There is significant difference in the mean gross profits between the different months of the year. Analysis of variance (ANOVA) was used to test this hypothesis. ANOVA is applied where we have more than 2 factors to be compared. We had twelve factors to be compared hence ANOVA was ideal test to be used. Results are presented in table 7 below; Table 7: Analysis of variance (ANOVA) for the gross profits versus months Profit Total Sum of Squares df Mean Square F Sig. Between Groups 35370.95 11 3215.54 3.867 .000 Within Groups 294370.01 354 831.55 Total 329740.95 365 From the ANOVA table above, it is evident that the null hypothesis is rejected (p-value 0.05) and as such we come to a conclusion that the gross profit significantly differs depending on the month of the year. How does sales performance compare between different seasons? The hypothesis tested for this research question is; Hypothesis 7: H0: There is no significant difference in the mean net sales between the different seasons. H0: There is significant difference in the mean net sales between the different seasons. Analysis of variance (ANOVA) was used to test this hypothesis. ANOVA is applied where we have more than 2 factors to be compared. We had four factors to be compared hence ANOVA was ideal test to be used. Results are presented in table 8 below; Table 8: Analysis of variance (ANOVA) for the net sales versus seasons Net_Sales Sum of Squares df Mean Square F Sig. Between Groups 487761.04 3 162587.01 1.658 .176 Within Groups 35496528.54 362 98056.71 Total 35984289.58 365 From the ANOVA table above, it is evident that the null hypothesis is not rejected (p-value 0.05) and as such we come to a conclusion that the net sales does not significantly differ depending on the season. Discussion of the results and recommendations Interesting findings came out of this study. First we were able to identify both the top performing products as well as the worst performing products. Some of the top performing products were drinks, water, vegetables, dairy products, fruits among others while the main products that were identified to perform poorly included; stock sauces, salad greens, spices, juicing products, snacks and herbal teas. Results showed that month of the year had no influence on the net sales of the company however it had significant influence on the gross profits of the company. Seasons also didnt have significant influence on the net sales. Location of the product in the shop had significant effect on the sales performance of the company. Based on the listed findings, it is evident that cost of goods varies depending on the month of the year hence affecting the gross profits of the company. It would therefore be advisable for the CEO of the Good harvest company to try understanding how the cost of goods compare within the different months. For instance, are the labour costs high in some months? Are the cost of materials higher in some months? Answering these questions will help the CEO to plan when to hire workers and when to make purchases of the materials to avoid doing it when the costs are high. By this the company will be able to maximize on its profit while minimizing of the expenditure costs. The CEO should also put much emphasis on ensuring that the display of the products is looked at in a more appropriate manner. Results showed that sales performance of the products varied depending on where the product was located in the shop. References Bagdonavicius, V., Nikulin, M. S. (2011). Chi-squared goodness-of-fit test for right censored data. The International Journal of Applied Mathematics and Statistics, 30-50. Chiang, C. L. (2003). Statistical methods of analysis, World Scientific. Cox, D. R. (2006). Principles of statistical inference. Derrick, B., Toher, D. White, P., 2017. How to compare the means of two samples that include paired observations and independent observations. The Quantitative Methods for Psychology, 13(2), p. 120126. Gelman, A., 2005. Analysis of variance? Why it is more important than ever. The Annals of Statistics, Volume 33, p. 153. Gelman, A., 2005. Analysis of variance? Why it is more important than ever. The Annals of Statistics, p. 153.