Discussion on Price and Purchase Indexes - Dissertation Example

ARETU: Discussion on Price and Purchase Indexes In Relation to TECCI incomes and Chignor area living standards June 7, 2006 [Insert [Insert Instructor] [Insert Class] ARETU This advisement is regarding TECCO as the dominant employer in Chignor area and the current state of economic affairs. ARETU has commissioned this assignment to disseminate truth in concern for the relative living conditions of members who live in the Chignor district and have witnessed a decline in conditions over a four year period. The index tables will show that there is a significant rate of inflation and that current pay scales of TECCO employees are not contusive to an adequate standard of living. The inflation increase is based on a comparison between 1999 and 2002 as well as a comparison of relative income of TECCO employees from 1999 to 2002. Price Index First we examine Table 1: Price Index (hand written Index in Appendix A) Table 1 Price Index Product Price/Units 1999 Index 2000 Index00 2001 Index01 2002 Index02 Vegetables Kilo 64 100 67 104.688 74 115.625 80 125 Meat Kilo 300 100 310 103.333 310 103.333 330 110 Alcohol Unit 125 100 129 103.2 145 116 154 123.2 Tobacco Pkt 199 100 206 103.518 220 110.553 240 120.603 Petrol Ltr 52 100 59 113.462 64 123.077 75 144.231 Housing Wk 4500 100 4590 102 4880 108.444 5000 111.111 There is a continuous inflation as years increase from the base of 1999, the strongest inflations being found in petroleum at 44%, vegetables at 25%, housing at 11% and meat products at 10%. Alcohol and tobacco prices have also increased by about 20% since 1999. This shows that prices on necessities such as food and housing have a dramatic increase over previous years. The average increases per year in comparison to 1999 are: Year Inflation % 2000 5.03 2001 12.83 2002 22.35 Significantly, we can assume that since 1999, there has been an overall inflation increase in pricing of 13.40% and more so that prices in 2002 are on average 22.35% higher than in 1999. Purchase Index Secondly, we want to determine the changes in purchasing habits of Chingor residents using the same base year of 1999, shown in Table 2: Purchase Index Table 2: Purchase Index Product Units 1999 Index 2000 Index00 2001 Index01 2002 Index02 Vegetables kilo 6 100 6 100 7 116.667 6 100 Meat kilo 4 100 4.5 112.5 4.75 118.75 5.3 132.5 Alcohol Unit 20 100 22 110 24 120 40 200 Tobacco Pkt 5 100 4 80 5 100 8 160 Petrol Ltr 25 100 27 108 26 104 40 160 Housing Wk. 1 100 1 100 1 100 1 100 There was an increase in vegetable sales in 2001, but as prices skyrocketed by 2002, sales fell away-being the only one to decrease in 2002. There are several inferences that can be made from this statement, the first being that people are not buying vegetables because of the cost, and the second being that since all other purchase categories increased, we can assume that family size also increased-this leaves a hole in healthy eating habits of our residents. Meat purchases increased by 32%, tobacco and petroleum by 60%. Probably the most disturbing inference to be made from this table and one that points to a serious problem for the quality of life in Chignor is that alcohol purchases have increased by 100%. Average purchasing increases show that since 1999, purchases increased dramatically in 2002. If we remove alcohol and tobacco as being unnecessary to a healthy lifestyle, the increase in 2002 is 23.25% compared to 1999, which is far more dramatic than previous years. This shows that meat and petroleum purchases have increased, which leads to the possibility that there are more people in the Chignor area, and raises a consideration that vegetable sales have actually decreased from 2001-2002, very possibly because TECCO employees can simply not afford to buy vegetables. Year Increase % 2000 1.75 2001 9.9 2002 42.08 Income Index Last, we need to examine the incomes of residents. In 2000-2001, there is a 6 percent increase in TECCO employees incomes from 1999, but there was not an increase from 2000 to 2001 (no pay raises). Furthermore, and possibly more disturbing, is that there was only a 10% income increase from 1999-20002, and this was only 4 % from 2001. Year 1999 2000 2001 2002 Earnings 100 6% 6% 10% Conclusions In the Chingor area, there has been a 22.35 % cost of living increase. Purchase habits, excluding alcohol, have increased 23.25%, and alcohol purchases by themselves have increased 100%. Earnings, however, have only increased by 10% over a four year period, which is barely half of the increases in the cost of living. The alcohol consumption level and tobacco purchase increase (60%) are relative to the conclusion that there has been a dramatic decline in the living standards of Chignor residents. Additional research is recommended to note if this is a national economic issue or specific to Chignor, and also further research into economic benchmarks, such as decline in automobile purchases (an indicator of economic health) against national averages. Furthermore, it becomes important for us to understand if the raise in alcohol purchases are due to a decline in the standards of living for TECCO employees, and lastly we must find a course of action to raise income levels to at least meet average prices, I would recommend fighting for an additional ten percent income increase. There is an inflation problem and an increase in purchases, but the income increase does not alleviate the pressure of low standards of living. It should be our focus to increase standards of living by fighting for a cost of living increase, but also we must recognise that money will not solve the problem of a 100% alcohol use increase, and therefore we should implement alcohol treatment and counseling plans as a secondary course of action to improve the standards of living. Appendix Appendix A: Manually Computed Table 1: Price Index Appendix B: Raw Tabular Data Table 1: Price of basic cost of living products in Chignor area 1999-2002 Product Units 1999 2000 2001 2002 Vegetables Price Per kilo 64 67 74 80 Meat Price per kilo 300 310 310 330 Alcohol Price per Unit 125 129 145 154 Tobacco Price per Pkt 199 206 220 240 Petrol Price per Ltr 52 59 64 75 Housing Rent per Wk. 4500 4590 4880 5000 Table 2: Average quantities purchased per week by Chignor households Product Units 1999 2000 2001 2002 Vegetables kilo 6 6 7 6 Meat kilo 4 4.5 4.75 5.3 Alcohol Unit 20 22 24 40 Tobacco Pkt 5 4 5 8 Petrol Ltr 25 27 26 40 Housing Wk. 1 1 1 1 Table 3: Index of Average earnings of TECCO employees Year 1999 2000 2001 2002 Earnings 100 106 106 110 Johnson's Chocolates: Relationships and Forecasts June 6, 2006 [Insert Name] [Insert Instructor] [Insert Class] Johnson's Chocolates: Year 2 In late December 2006, Johnson's Chocolates is looking ahead to production, marketing and financial schedules. The following statistical inferences are made from the 3 years past data from Johnson's Chocolates on a consultancy basis. As part of chocolate sales, understanding the relationships between buyers and product is important. Currently, there are two conflicting views: (a) Product sales are in relation to USA airplane departures, and (b) Product sales are in relation to Japan airplane departures. Using the information of sales numbers and departures, we will first define the strength of the relationship between USA departures and sales as well as Japan departures and sales. The next information to be discovered is a workable 12 month forecast for 2007 based on previous 3 year sales data. This will be found using statistical inferences and graphing the found information for easy reading. Finally, we will look at some recommendations based on production, marketing and financing. To describe the relationships between the information we have and the inferences we are making, a preliminary description of the data is uses. Chart titled Sales by Month shows the total amount of sales for each month in different colors and grouped by year. Sales and Departure Relationships The first step in our research it to find out if Johnson's Chocolate sales are dependent on USA and/or Japanese outgoing flights. We have conflicting evidence here, in which some managers feel there is a strong relationship between sales and USA departures, where others feel the same in regards to Japanese departures. It is important to understand that correlation research is a mathematical description that defines the relationship value between two components-in our case, Sales and Departures. Correlations are described by a linear regression model, which is a line on a graph that shows to what numerical degree Sales is affected by Departures from both countries. Correlation statistics are defined by scatter plots and linear regression equations to represent the relationship, but correlation is mainly described using a correlation coefficient. The correlation coefficient is a number between -1.00 and +1.00, where -1.00 indicates there is not a relationship between the two variables, and +1.00 indicates a high relationship between the two variables. The significant benefit is to Johnson's Chocolates is to understand how to further marketing and product distribution, however, it is very important to understand that this can not describe a cause and effect relationship; it is only an observation of the quantitative values associated with a variable. This means that finding out that Sales are affected by a countries departures does not explain why there is a relationship, and those are factors that marketing research would conclude, such as sales, promotions, proximity, time of year, quality, the stores relationship with the customer, and so on. I have to explain that we can only describe a correlation between Sales and Departures by country for the year 2006 because Departure information is only given for 2006, significantly, this is not enough year information to define a trend in the relationship over years, but only for 2006. Defining a Correlation between Sales in 2006 and Departures The correlation coefficients for sales with departures as the predictor are: USA 0.639743 Japan 0.765039 This indicates that yes, there is a relationship between sales and departures of each country, with Japan having a more positive relationship than USA. We touched a bit earlier on linear regression; this is the plotted line that shows how sales are affected by an increase in departures. The first Graph is based on USA departures: Graph 1: USA Departures The second graph shows how sales are positively affected by Japanese departures: Graph 2: Japan Departures As you can see, as either USA or Japan travel increases, sales also increase. This shows that there is a strong relationship between both countries and Johnson's Chocolates sales. Recall that the correlation coefficient for the USA was 0.639743, and that for Japan the correlation coefficient is 0.765039. There are two important inferences from this. The first is that there is a positive relationship, and the second is that Japanese departures have a greater probability of affecting sales compared to USA. This is a marketing opportunity, because the USA actually has more volume of departures than Japan, and therefore it can be concluded that Johnson's Chocolates should market more towards USA patrons while maintaining a relationship with Japanese patrons. Forecasts for 2007 In forecasting, we first want to examine the time series data plot using a linear graph. The Time Series Plot of 2004, 2005, 2006 describes the movement of sales across each month by year. This allows us to look at the differences between the months and their relationship to sales within each of the three year time frames. As a second part of our analysis, we want to forecast Johnson's Chocolate sales for 2007. The moving average shows the average amount of sales across each year. Moving averages are generally used to measure momentum and define areas of possible support and resistance. The Moving Average Table 2004- 2006 shows that as the year moves forward, the momentum increases with 134.9 being the average across the time series. Moving Average Table 2004-2006 MAPE 66.2 MAD 134.9 MSD 25308.9 Time Sales Moving Average Predictor Error 2004 Jan 70 * * * Feb 110 * * * Mar 142 * * * Apr 325 * * * May 285 * * * Jun 260 198.667 * * Jul 320 240.333 198.667 121.333 Aug 358 281.667 240.333 117.667 Sep 395 323.833 281.667 113.333 Oct 420 339.667 323.833 96.167 Nov 496 374.833 339.667 156.333 Dec 506 415.833 374.833 131.167 2005 Jan 75 375.000 415.833 -340.833 Feb 123 335.833 375.000 -252.000 Mar 200 303.333 335.833 -135.833 Apr 279 279.833 303.333 -24.333 May 305 248.000 279.833 25.167 Jun 276 209.667 248.000 28.000 Jul 353 256.000 209.667 143.333 Aug 377 298.333 256.000 121.000 Sep 419 334.833 298.333 120.667 Oct 468 366.333 334.833 133.167 Nov 550 407.167 366.333 183.667 Dec 506 445.500 407.167 98.833 2006 Jan 89 401.500 445.500 -356.500 Feb 142 362.333 401.500 -259.500 Mar 195 325.000 362.333 -167.333 Apr 345 304.500 325.000 20.000 May 344 270.167 304.500 39.500 Jun 317 238.667 270.167 46.833 Jul 376 286.500 238.667 137.333 Aug 410 331.167 286.500 123.500 Sep 468 376.667 331.167 136.833 Oct 497 402.000 376.667 120.333 Nov 645 452.167 402.000 243.000 Dec 506 483.667 452.167 53.833 The third part of the analysis is similar to what we looked at before in correlations, the linear regression. This shows how the moving average explained above works in each month's time line. Finally, we know that the linear regression equation is: Yt = 213.129 + 6.42548*t, shown by the table above. This equation allows us to solve for Y, where Y is sales and t is the month. Using this equation, we forecast for a twelve month period in 2007. The final chart titled Forecast shows the sales for each month by years 2004-2006. The last line, 2007, is the equation explained above. This plots the forecast for 2007. At the bottom of the chart we show the raw data for each sales month and year, with the final data being the forecast for 2007. Final Recommendations 1. Production Production wise, as the time line nears the lower sales times (Jan-April) Johnson's should take the initiative to ensure that production techniques and qualities are viable and, most importantly, consistent. This will help Johnson's Chocolates prepare for summer and Christmas travelers by examining what components of production can be improved. First, I would recommend describing the quality of production techniques and completing an analysis to find what components in production can be improved on before the rush months. Some things to consider are measured weights of boxes as well as costs of production and logical sequences of manufacturing. 2. Marketing As we saw above, there is a relationship between the type of patron's departure and sales in airports. Furthermore, we can conclude that USA travel is quite a bit more than Japanese travel, and that forecasting shows a marked upward trend in sales. The focus for marketing is to develop a customer relationship with airport departures, especially in the winter months where we see the strongest forecasted numbers for sales. Some special marketing procedures then could be towards the holiday season and traveling memories that deliver a special taste-even when you go home! It may be possible to develop a special flavor of British Gold directed at USA consumers to remind them of their holiday in the UK. 3. Financial Financial forecasting for 2007 is respectively better than previous years. The plotted line in the above Forecast chart shows that 2007 will have some marked sales increases, especially in the winter months. This is great news for Johnson's Chocolates. In financing options, especially in relationship to marketing capability, Johnson's Chocolates should look at the costs of new marketing for special winter memories A few ideas here are to determine the current balance of equity and assets to determine where Johnson's can create new avenues of funding against futures (of sales). In conclusion, the statistical data shows that Johnson's has a bright future indeed, and that marketing towards that future-USA and Winter Holiday-will be a core competency in further developing Johnson's Chocolates. Appendix Appendix A: Raw Data Month 2004 2005 2006 USA JAPAN January 70 75 89 140235 23674 February 110 123 142 130275 34526 March 142 200 195 155786 43789 April 325 279 345 178765 45678 May 285 305 344 189642 59842 June 260 276 317 200761 67549 July 320 353 376 220673 70452 August 358 377 410 221896 74200 September 395 419 468 168901 74912 October 420 468 497 170456 59841 November 496 550 645 180457 65489 December 506 506 506 230561 70951 Appendix B: Correlation Inferences Regression Analysis: 2006 versus USA The regression equation is 2006 = - 299.6 + 0.003714 USA S = 149.861 R-Sq = 40.9% R-Sq(adj) = 35.0% Analysis of Variance Source DF SS MS F P Regression 1 155596 155596 6.93 0.025 Error 10 224582 22458 Total 11 380178 Regression Analysis: 2006 versus JAPAN The regression equation is 2006 = - 109.6 + 0.008464 JAPAN S = 125.565 R-Sq = 58.5% R-Sq(adj) = 54.4% Analysis of Variance Source DF SS MS F P Regression 1 222513 222513 14.11 0.004 Error 10 157666 15767 Total 11 380178 Regression Analysis: 2006 versus USA, JAPAN The regression equation is 2006 = - 148 + 0.00041 USA + 0.00784 JAPAN Predictor Coef SE Coef T P Constant -147.9 242.6 -0.61 0.557 USA 0.000407 0.002091 0.19 0.850 JAPAN 0.007841 0.003984 1.97 0.081 S = 132.080 R-Sq = 58.7% R-Sq(adj) = 49.5% Analysis of Variance Source DF SS MS F P Regression 2 223173 111587 6.40 0.019 Residual Error 9 157005 17445 Total 11 380178 Source DF Seq SS USA 1 155596 JAPAN 1 67577 Appendix C: Forecasting Inferences Multiple Correspondence Analysis: 2004, 2005, 2006, Month Analysis of Indicator Matrix Axis Inertia Proportion Cumulative Histogram 1 1.0000 0.0909 0.0909 ****************************** 2 1.0000 0.0909 0.1818 ***************************** 3 1.0000 0.0909 0.2727 ***************************** 4 1.0000 0.0909 0.3636 ***************************** 5 1.0000 0.0909 0.4545 ***************************** 6 1.0000 0.0909 0.5455 ***************************** 7 1.0000 0.0909 0.6364 ***************************** 8 1.0000 0.0909 0.7273 ***************************** 9 1.0000 0.0909 0.8182 ***************************** 10 1.0000 0.0909 0.9091 ***************************** 11 1.0000 0.0909 1.0000 ***************************** Total 11.0000 Column Contributions Component 1 Component 2 ID Name Qual Mass Inert Coord Corr Contr Coord Corr Contr 1 Column1 0.047 0.021 0.021 -0.540 0.026 0.006 0.470 0.020 0.005 2 Column2 0.519 0.021 0.021 2.370 0.510 0.117 -0.308 0.009 0.002 3 Column3 0.125 0.021 0.021 -0.918 0.077 0.018 -0.728 0.048 0.011 4 Column4 0.038 0.021 0.021 0.458 0.019 0.004 0.454 0.019 0.004 5 Column5 0.366 0.021 0.021 -1.135 0.117 0.027 -1.655 0.249 0.057 6 Column6 0.300 0.021 0.021 0.657 0.039 0.009 1.692 0.260 0.060 7 Column7 0.100 0.021 0.021 -0.902 0.074 0.017 0.540 0.026 0.006 8 Column8 0.103 0.021 0.021 0.180 0.003 0.001 1.049 0.100 0.023 9 Column9 0.437 0.021 0.021 1.048 0.100 0.023 -1.925 0.337 0.077 10 Column10 0.147 0.021 0.021 -1.173 0.125 0.029 0.488 0.022 0.005 11 Column11 0.001 0.021 0.021 -0.046 0.000 0.000 -0.090 0.001 0.000 12 Column12 0.000 0.021 0.021 0.000 0.000 0.000 0.014 0.000 0.000 13 Column13 0.047 0.021 0.021 -0.540 0.026 0.006 0.470 0.020 0.005 14 Column14 0.519 0.021 0.021 2.370 0.510 0.117 -0.308 0.009 0.002 15 Column15 0.125 0.021 0.021 -0.918 0.077 0.018 -0.728 0.048 0.011 16 Column16 0.038 0.021 0.021 0.458 0.019 0.004 0.454 0.019 0.004 17 Column17 0.100 0.021 0.021 -0.902 0.074 0.017 0.540 0.026 0.006 18 Column18 0.366 0.021 0.021 -1.135 0.117 0.027 -1.655 0.249 0.057 19 Column19 0.300 0.021 0.021 0.657 0.039 0.009 1.692 0.260 0.060 20 Column20 0.103 0.021 0.021 0.180 0.003 0.001 1.049 0.100 0.023 21 Column21 0.437 0.021 0.021 1.048 0.100 0.023 -1.925 0.337 0.077 22 Column22 0.147 0.021 0.021 -1.173 0.125 0.029 0.488 0.022 0.005 23 Column23 0.000 0.021 0.021 0.000 0.000 0.000 0.014 0.000 0.000 24 Column24 0.001 0.021 0.021 -0.046 0.000 0.000 -0.090 0.001 0.000 25 Column25 0.047 0.021 0.021 -0.540 0.026 0.006 0.470 0.020 0.005 26 Column26 0.519 0.021 0.021 2.370 0.510 0.117 -0.308 0.009 0.002 27 Column27 0.125 0.021 0.021 -0.918 0.077 0.018 -0.728 0.048 0.011 28 Column28 0.038 0.021 0.021 0.458 0.019 0.004 0.454 0.019 0.004 29 Column29 0.366 0.021 0.021 -1.135 0.117 0.027 -1.655 0.249 0.057 30 Column30 0.100 0.021 0.021 -0.902 0.074 0.017 0.540 0.026 0.006 31 Column31 0.300 0.021 0.021 0.657 0.039 0.009 1.692 0.260 0.060 32 Column32 0.103 0.021 0.021 0.180 0.003 0.001 1.049 0.100 0.023 33 Column33 0.437 0.021 0.021 1.048 0.100 0.023 -1.925 0.337 0.077 34 Column34 0.147 0.021 0.021 -1.173 0.125 0.029 0.488 0.022 0.005 35 Column35 0.000 0.021 0.021 -0.000 0.000 0.000 0.014 0.000 0.000 36 Column36 0.001 0.021 0.021 -0.046 0.000 0.000 -0.090 0.001 0.000 37 Column37 0.047 0.021 0.021 -0.540 0.026 0.006 0.470 0.020 0.005 38 Column38 0.519 0.021 0.021 2.370 0.510 0.117 -0.308 0.009 0.002 39 Column39 0.125 0.021 0.021 -0.918 0.077 0.018 -0.728 0.048 0.011 40 Column40 0.100 0.021 0.021 -0.902 0.074 0.017 0.540 0.026 0.006 41 Column41 0.366 0.021 0.021 -1.135 0.117 0.027 -1.655 0.249 0.057 42 Column42 0.038 0.021 0.021 0.458 0.019 0.004 0.454 0.019 0.004 43 Column43 0.300 0.021 0.021 0.657 0.039 0.009 1.692 0.260 0.060 44 Column44 0.103 0.021 0.021 0.180 0.003 0.001 1.049 0.100 0.023 45 Column45 0.437 0.021 0.021 1.048 0.100 0.023 -1.925 0.337 0.077 46 Column46 0.147 0.021 0.021 -1.173 0.125 0.029 0.488 0.022 0.005 47 Column47 0.001 0.021 0.021 -0.046 0.000 0.000 -0.090 0.001 0.000 48 Column48 0.000 0.021 0.021 -0.000 0.000 0.000 0.014 0.000 0.000 Trend Analysis Fitted Trend Equation Yt = 213.129 + 6.42548*t AccuracyMeasures MAPE 55.5 MAD 107.0 MSD 16871.6 Forecasts Period Forecast 1 179.333 2 215.333 3 251.333 4 287.333 5 323.333 6 359.333 7 395.333 8 431.333 9 467.333 10 503.333 11 539.333 12 575.333 Regression Analysis: Sums versus Month The regression equation is Sums = - 152657 + 3.95 Month Predictor Coef SE Coef T P Constant -152657 13127 -11.63 0.000 Month 3.9515 0.3376 11.70 0.000 S = 122.808 R-Sq = 93.2% R-Sq(adj) = 92.5% Analysis of Variance Source DF SS MS F P Regression 1 2066287 2066287 137.01 0.000 Residual Error 10 150817 15082 Total 11 2217104 Unusual Observations Obs Month Sums Fit SE Fit Residual St Resid 4 38808 949.0 693.7 43.9 255.3 2.23R R denotes an observation with a large standardized residual. Appendix D: Sales Table with Period Forecast Month 2004 2005 2006 Period Forecast 2007 January 70 75 89 179.333 February 110 123 142 215.333 March 142 200 195 251.333 April 325 279 345 287.333 May 285 305 344 323.333 June 260 276 317 359.333 July 320 353 376 395.333 August 358 377 410 431.333 September 395 419 468 467.333 October 420 468 497 503.333 November 496 550 645 539.333 December 506 506 506 575.333 Memo To: Matt and Michelle From: [INSERT NAME] Date: February 13, 2012 Re: Forecasted Values Actual sales of 250 gram "British Gold" for last 6 months compared to 2007 forecast: Month Actual Sales Period Forecast 2007 January 76 179.333 February 148 215.333 March 219 251.333 April 239 287.333 May 267 323.333 June 287 359.333 The 2007 forecast exceeded actual sales for the first six months of 2007. There becomes a need to re-evaluate the presumed forecasting modeled previously. A secondary analysis shows the constant to be -100.10, which infers that on average, expected sales were 100 basis points ahead of actual sales. This can be due to many factors, included economic and marketing. The new regression equation is Actual Sales = - 100 + 1.14 Period Forecast 2007. I recommend a new forecast because there is such a large deviation from the original forecast to the real data. Effectively, this would infer that new forecasts for the remainder 6 months: Month Period Forecast 2007 July 251.333 August 285.375 September 315.906 October 342.014 November 363.447 December 380.458 It is recommended to examine the changes in 2007 and make appropriate alteration in production and financing while maintaining previously described marketing recommendations. Forecasting is a statistical response to previous information. There has been an upward trend until 2007 in Johnson's sales. At this juncture, it is important to note that the upward trend we described six months ago is not as strong as assumed. Now, Johnson's should prepare for the downward trend that is being experienced in chocolate sales. Based on this conclusion, the following recommendations are to examine the possible conditions that affect the forecasted sales model. First, an objective observation of economic trends-are other airline gift based companies facing the same lowered sales This will allow Johnson's to make adequate forecasts based on the financial status of customers and competitions. In regards to this, it would also be a good idea to examine trends and changes in travel, especially in the USA and Japan departures to find if there has been a significant reduction in airline customers, Johnson's biggest consumer. An analysis of production trends in quality control will allow Johnson's to discover if the loss in proposed sales is due to quality or packaging and is an issue that can be internally controlled. If there were changes made recently in production and manufacturing, the sequence and quality should be examined. Lastly, it would be recommended to find any changes in marketing strategy that may have been applied and may not be working according to plan. This could be because marketing put emphasis on a lowered customer base or because there is not enough emphasis on marketing to airline consumers. In conclusion, it is important to understand that forecasting is not an exact science. Numbers can be predicted to a best fit, but in truth, reality does not always mimic statistics because there are many factors which alter assumed trends in data. Appendix A shows the statistical inferences that were made for the above 6 month forecast, and Appendix B shows the new linear regression model based on the regression equation is Actual Sales = - 100 + 1.14 Period Forecast 2007. Appendix Appendix A: Regression Analysis: Actual Sales versus Period Forecast 2007 The regression equation is Actual Sales = - 100 + 1.14 Period Forecast 2007 Predictor Coef SE Coef T P Constant -100.10 45.95 -2.18 0.095 Period Forecast 2007 1.1365 0.1663 6.83 0.002 S = 25.0468 R-Sq = 92.1% R-Sq(adj) = 90.1% Analysis of Variance Source DF SS MS F P Regression 1 29295 29295 46.70 0.002 Residual Error 4 2509 627 Total 5 31804 Appendix B: Linear Regression Plot Johnson's Chocolate Machine Problems Analysis of Batch 112 June 6, 2006 [Insert Name] [Insert Instructor] [Insert Class] Basic Analysis of Batch 112 Batch 112 was the preceding batch of sold chocolates for Johnson's Chocolates. This batch is described by weight of each box, and shown in Chart 1: Chocolates by Box The statistical test is find if is a significant deviation from the 250 gram mark, in this case for production purposes we want to decide if there is a significant probability that weights of chocolate are less than 250 grams. There are 36 weighed boxes in this sample. 223 grams is the lowest weighed box, and the maximum value is 265.8 grams. The first test is to find the measures of central tendency. These are the mid ranges of the weights. Mean is the average weight which approximates the statistical norm, and the mean weight is 250.32, which is very close to the constant weight of 250 grams we are trying to reach. Median is the mid point value, the number exactly in the middle of the thirty six different weights. The median is also 250.3, which means that all other weights are either above or below it. Mode is the weight that is recorded the most. The mode is 246.9, which is the most recorded value, and lower than the mean we are trying to reach consistently. The standard error measures the variance between values; in this case the average variance between each box weight is 1.219. The standard deviation measures the distribution for the group of scores, meaning that it is assumed mathematically that 2/3rds of the scores are within 7.135 grams of each other. The range is the difference between the maximum and minimum scores of 42.8 grams. Lastly, the confidence level shows to what degree we can be certain that the estimates are close to the true value, here we have a 95 percent standard confidence level that a weight will be within 2.47 grams of its true weight, and that weight will occur in intervals of plus or minus 0.076 grams. Basically, these confidences define how likely it is that boxes of chocolates will have the same result as the described weight. With our confidence level of 2.47 grams and intervals of 0.076 grams, we find level to set automatic weighing machine to be calibrated at to ensure 95% confidence level needs to be within 0.076 grams of true weight. These are shown by category in Table 1: Statistical Inferences. Table 1: Statistical Inferences Chocolate Mean 250.3277778 Standard Error 1.219234805 Median 250.3 Mode 246.9 Standard Deviation 7.31540883 Range 42.8 Minimum 223 Maximum 265.8 Count 36 Confidence Level(95.0%) 2.475178228 Confidence Interval 0.076454 Problem of Production Errors We want to test the probability that a weight will be 250 grams, 245 grams or 239 grams. Normal distribution is a statistical term that measures the frequency of an occurrence-in our case, weight-against the mean of 250 grams. This allows us to understand how often we can expect a weight to be less than or equal to 250 grams. The hypothesis in this experiment is that average weights are less than 250 grams in a significant number, this is written as: H0 < 250. Normal Distributions A normal distribution runs along a bell shaped curve of probabilities, the further away from the mean the smaller possibility of the weight being different. 245 grams is so close to 250 grams that there is a greater chance a box will weigh 245 grams than the chance it will weigh 239 grams. Table 2: Normal Distributions 239 Grams 0.060753 245 Grams 0.233216 250 Grams 0.482131 255 Grams 0.261515 266 Grams 0.016082 Specifically, normal distribution means that every time we sell a box of chocolates, there is a 48 percent chance that it will weigh 250 grams, with a twenty-six percent chance it will weigh 255 grams and a one percent chance it will weigh 266 grams, which points to the fact that while we have some large weights, there is not enough of a probability towards heavy boxes compared to light boxes. In turn, this infers that chocolates are not being over weighed to a detrimental loss. There is a 23 percent chance it will weigh 245 grams, and a 6 percent chance it will weigh 239 grams. The normal probability distribution is shown in Appendix B: Normal Probability Distributions. A p-value describes how likely it is that the low weights were random and not significant to the experiment, this number is the basis for analyzing a z-test. The p-value is measured against an alpha of 0.05, or a five percent confidence that it is not random. This means that if the p-value is higher than 0.05, the test is not random and we can accept the significance of the numbers. The p-value is 0.78814, so the tests are significant and not random figures. Now, we use a z-test to determine at which range we reject or accept the hypothesis. A z-value is used to if we accept or reject that weights have a strong possibility of being less than 250 grams. The z-value = 0.394027, this is computed using the standard deviations and normal distributions of the sample test. The z-value is compared to a z-table, a table that contains percentages of an area under the normal curve between the mean and the z score, and indicates at which point we accept or reject our hypothesis above. Because the z-score is less than the z-table value of 1.645, we can accept that the hypothesis is true, and there is a significant level of chocolate boxes that will weigh less than 250 grams. Recommendations for Quality Control We now know that there is a significance of the data, which means that there is a strong possibility that 29 % box weights will be less than 250 grams. This brings us to the conclusion that quality control and measurements are not effective enough to prevent poor customer experiences. To alleviate that, Johnson's Chocolates should seek to encourage and implement better quality control procedures by examining equipment and procedures. Tools for quality control are examining the reliability, maintainability and safety of production. To know how to develop better quality control, further research in the tools, manufacturing, machinery and deployment process would first be recommended. Johnson's should examine the infrastructure of processing and distribution within the plant to determine how functionality is limited by elements such as controls, processes performance and control integrity. Furthermore, it becomes necessary to examine not only the machinery, but the methods under which that machinery and process are developed and utilized by plant management and personnel. Until a point of viable reliability is reached, a consideration lends to a longitudinal analysis of chocolate box weights with a sample of the population of chocolates sold over a six month period. Alternative analysis shows that over a six month period. Johnson's has 1216 sales, and the sampling size should be 40 for accurate data. Appendix Appendix A: Raw Data Batch 112: 250 249 251.2 258 251.7 255 246.9 248.1 245.9 245.8 252 256.8 251 247.5 255 246.9 249.7 251.5 247 265 246.9 257.6 249.9 248.6 253.8 251.9 223 255.9 258 245.9 250 240.1 251 238.8 265.8 250.6 Appendix B: Normal Probability Distributions Read More