Vice-president Arun Mittra speculates: We have always estimated how many transformers will be needed to meet demand. The usual method is to look at th

Vice-president Arun Mittra speculates: We have always estimated how many transformers will be needed to meet demand. The usual method is to look at the sales figures of the last two to three months and also the sales figures of the last two years in the same month. Next make a guess as to how many transformers will be needed. Either we have too many transformers in stock, or there are times when there are not enough to meet our normal production levels. It is a classic case of both understocking and overstocking.Ratnaparkhi, operations head, has been given two charges by Mittra. First, to develop an analysis of the data and present a report with recommendations. Second, “to come up with a report that even a lower grade clerk in stores should be able to fathom and follow.”In an effort to develop a report that is understood by all, Ratnaparkhi decides to provide incremental amounts of information to his operations manager, who is assigned the task of developing the complete analyses.A-Cat Corporation is committed to the pursuit of a robust statistical process control (quality control) program to monitor the quality of its transformers. Ratnaparkhi, aware that the construction of quality control charts depends on means and ranges, provides the following descriptive statistics for 2006 (from Exhibit 1).2006Mean 801.1667Standard Error 24.18766Median 793Mode 708Standard Deviation 83.78851Sample Variance 7020.515Kurtosis -1.62662Skewness 0.122258Range 221Minimum 695Maximum 916Sum 9614Count 12The operations manager is assigned the task of developing descriptive statistics for the remaining years, 2007–2010, that are to be submitted to the quality control department.A-Cat’s president asks Mittra, his vice-president of operations, to provide the sales department with an estimate of the mean number of transformers that are required to produce voltage regulators. Mittra, recalling the product data from 2006, which was the last year he supervised the production line, speculates that the mean number of transformers that are needed is less than 745 transformers. His analysis reveals the following:t = 2.32p = .9798This suggests that the mean number of transformers needed is not less than 745 but at least 745 transformers. Given that Mittra uses older (2006) data, his operations manager knows that he substantially underestimates current transformers requirements. She believes that the mean number of transformers required exceeds 1000 transformers and decides to test this using the most recent (2010) data.Initially, the operations manager possessed only data for years 2006 to 2008. However, she strongly believes that the mean number of transformers needed to produce voltage regulators has increased over the three-year period. She performs a one-way analysis of variance (ANOVA) analysis that follows:2006 2007 2008779 845 857802 739 881818 871 937888 927 1159898 1133 1072902 1124 1246916 1056 1198708 889 922695 857 798708 772 879716 751 945784 820 990Anova: Single FactorSUMMARYGroups           Count                         Sum    Average         Variance2006               12                    9614 801.1667       7020.5152007               12                    10784 898.6667       18750.062008               12                    11884 990.3333       21117.88ANOVASource of Variation             SS                   df         MS                  F                      P-value          F critBetween Groups      214772.2       2          107386.1       6.870739       0.003202       3.284918Within Groups          515773           33        15629.48Total                           730545.2       35The results (F = 6.871 and p = 0.003202) suggest that indeed the mean number of transformers has changed over the period 2006–2008. Mittra has now provided her with the remaining two years of data (2009 and 2010) and would like to know if the mean number of transformers required has changed over the period 2006–2010.Finally, the operations manager is tasked with developing a model for forecasting transformer requirements based on sales of refrigerators. The table below summarizes sales of refrigerators and transformer requirements by quarter for the period 2006–2010, which are extracted from Exhibits 2 and 1 respectively.Sales of Refrigerators         Transformer Requirements3832 23995032 26883947 23193291 22084007 24555903 31844274 28023692 23434826 26756492 34774765 29184972 28145411 28747678 37745774 32476007 31076290 27768332 35716107 33546792 3513III. Identify statistical tools and methods to collect data:A. Identify the appropriate family of statistical tools that you will use to perform your analysis. What are your statistical assumptions concerning the data that led you to selecting this family of tools? In other words, why did you select this family of tools for statistical analysis?B. Determine the category of the provided data in the given case study. Be sure to justify why the data fits into this category type. What is the relationship between the type of data and the tools?C. From the identified family of statistical tools, select the most appropriate tool(s) for analyzing the data provided in the given case study.D. Justify why you chose this tool to analyze the data. Be sure to include how this tool will help predict the use of the data in driving decisions.E. Describe the quantitative method that will best inform data-driven decisions. Be sure to include how this method will point out the relationships between the data. How will this method allow for the most reliable data?IV. Analyze data to determine the appropriate decision for the identified problem:A. Outline the process needed to utilize your statistical analysis to reach a decision regarding the given problem.B. Explain how following this process leads to valid, data-driven decisions. In other words, why is following your outlined process important?C. After analyzing the data sets in the case study, describe the reliability of the results. Be sure to include how you know whether the results are reliable.D. Illustrate a data-driven decision that addresses the given problem. How does your decision address the given problem? How will it result in operational improvement?

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