Statistics Problems - Assignment Example

STATISTICS PROBLEMS Location Statistics Problems Problem one i. Dataset:(check appendices) ii. a. In this problem, a sample of 14 Samsung phones was randomly selected from a wide range of phones from the carphone warehouse website. This sample was preferred because the phones were selected from a population of Samsung phones that follows a normal distribution. When the population follows a normal distribution or the sample selected is tested to follow a normal distribution, there is no need to pick a very huge sample to proceed in the analysis. However the population is not normally distributed, we have to select a sample at least 30 to confirm with the theory of the law of large numbers or the central limit theory. Otherwise, it will entail the use of the non-parametric method of analysis. On the contrary some researchers choose to employ the solvency formula of sample size selection although this has got the shortcoming that it cannot be used when the population size is unknown. The sample size of 14 was proffered because the population was normally distributed and for minimization of the cost associated with data mining. b. The choice for selection of only Samsung phones was to eliminate the variation that would arise because of differences in the brands. Consequently, all the other phones were excluded from the analysis. There seems to be a huge variation among the phone of different brand for instance an IPhone mobile the same screen size and capacity as the Samsung could have a data consuming capacity far different from the former. So to reduce the defects that would occur in the analysis because of this variation due to the phone brands, only the Samsung phones were selected in this study. Secondly, the Samsung phones have phone sizes and categories in almost all the sizes. Their phones have screen sizes that can cover a wide range as compared to the IPhone. This Variety in the Samsung phones is very important since it increases the scope of analysis. c. Although the assumption of normality is assumed in this analysis, the sample size is not big enough. iii. The graph above shows the distribution and consequent initial relationship between the two variables with the price of the phones. The plots show that the there exists a positive relationship between camera pixels and price of data. Similarly, the exists a positive relationship between the screen and price of data. The plot above shows a visual display of the primary relationship between the variables in the model before conducting the regression and correlation analysis. There exists a relationship between the camera pixels and screen size. Correlations screen_size camera_pixels price_of_data screen_size Pearson Correlation 1 .868** .725** Sig. (2-tailed) .000 .003 N 14 14 14 camera_pixels Pearson Correlation .868** 1 .872** Sig. (2-tailed) .000 .000 N 14 14 14 price_of_data Pearson Correlation .725** .872** 1 Sig. (2-tailed) .003 .000 N 14 14 14 **. Correlation is significant at the 0.01 level (2-tailed). The table shows that there exists a significant relationship between the monthly data prices and screen size of the phones. The correlation coefficient was tested to be significant at 0.05 level of significance. Similarly, there exists a significant relationship between the camera pixels and the price variable. The two independent variables in the model also have a very significant relationship. Coefficients Model Unstandardized Coefficients Standardized Coefficients t Sig. Collinearity Statistics B Std. Error Beta Tolerance VIF 1 (Constant) 9.203 25.822 .356 .728 screen_size -3.063 7.078 -.127 -.433 .674 .247 4.045 camera_pixels 2.884 .863 .983 3.342 .007 .247 4.045 a. Dependent Variable: price_of_data From the above regression results, the following regression equation was obtained price_of_data=9.203+2.884 camera_pixels-3.063 screen_size The regression results show that the screen size is negatively related to the price of the phones; this coefficient was not significant at 0.06 since it reported a p-value greater than the level of significance. The regression results further indicated a positive relationship between the camera pixels and the monthly data charges. It was tested to be significant as implied by a p-value lower than the level of significance. iv. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .875a .765 .722 7.46037 a. Predictors: (Constant), camera_pixels, screen_size The table above showed that R-squared value from this regression was 87.5% that implies that the two independent variables explain 87.5% of the variation in the dependent variable. Thus, these two variables are a good predictor of the monthly prices. Problem two: a. Level of significance=0.05 Ho: =60 H1: 60 N-1=139-1=138 N-1 =67.3=lower boundary  N-1=74.2=upper boundary Since 60 those not lie between the lower and upper boundary, we reject the null hypothesis b. A B C D E F G H 39 43 42 40 38 41 42 40 Level of significance=0.05 Ho: Mean= 41 H1: Mean41 Error= =1.96*(1.685/2.8284) Error=1.1676 Lower bound= ( Upper bound = Since 40 is within that range, we fail to reject null hypothesis Problem three: The sigma six is simply a set of different methods and statistical tools that are used for a number of process improvement undertakings. Motorola company first introduced the technique of sigma six in the year 1986.Jack Welch made sigma six very central to his business Strategy at general electric in the year 1995.Today the sigma six techniques are widely applied in the in the industrial sector. The method mainly seeks to make an improvement in the quality control processes by making proper identification of the major causes of errors that could are incurred during the production process. The technique is normally applied by the quality control personnel to help them in controlling the major defects that could arise in the production process. It is very helpful in the bid to remove the errors and minimizing unnecessary variations and deviations in the manufacturing and business processes. Sigma Six mainly uses the quality management methods like the empirical approaches together with very numerous statistical methods and approaches. The method creates an infrastructure of people within the organization that are experts in these methods. Each of the six-sigma projects that are carried out in any given organization will always follow predefined sequential steps. These processes should possess quantifiable value targets. For instance reduction of the various process cycles time, reduction in the levels of pollution. It further entails a reduction in the costs, the overall increase in the customer satisfaction motifs and finally to increase the profits of the companies that employ this technique. The use of sigma six mainly forms the terminology associated with the manufacturing process. It mainly deals with the terms closely associated with precise statistical data modeling frameworks in the manufacturing process. Thus, the maturity of the entire manufacturing process can be described in simple terms using the proper sigma ratings. These ratings should also indicate the company’s yields or the percentage of the defect-free products that it will create. Any appropriate sigma six techniques should be a process in which 99.99966% of all the available opportunities to produce a given output are statistically expected to be free of the defects. This defect if at all it surfaces should be less than 4.5 sigma level. Motorola set the sigma six for all of the manufacturing processes in their company and all of its manufacturing operations. The term sigma six comes from the vast field of statistics and is used in the statistical quality control mechanisms that also go an extra mile of evaluating the process capability. Initially, the sigma six merely referred to the manufacturer’s ability to produce a significant proportion of the products within the required specifications with little or limited variability and deviance. The processes that use the sigma six qualities in the short term are assumed to produce defect levels below 3.4 in the end. The implicit goal of sigma six mechanisms is to make improvements to all the processes but not necessarily to the 3.4 DPMO level. The organizations thus need properly to determine the appropriate level of sigma six for all of the most important and crucial processes and attempt to achieve all of these. Because of this objective, sigma six is mainly aiming at proper management of the organizations in the appropriate prioritization of the possible areas of improvement. In the last few years, most practitioners devised ways of combining the ideas of Sigma sixth with the concept of lean manufacturing to develop another methodology called Lean Six Sigma. The method of lean six sigma views the procedure of lean manufacturing. It addresses process flow and a number of waste issues in the production process and sigma six. It mainly focuses on the variation and proper design as the major accompanying disciplines that aimed at promoting good business and Excellency in the operations. A number of companies like Verizon, IBM, GE, and GENPACT widely use the lean six-sigma methodologies in a bid to focus their transformations and efforts on efficiency and growth as well. The lean sigma serves as a primary foundation regarding innovation thought the entirety of the organization, right from manufacturing and the development of the software solutions. Another application of sigma six is in the instance of absolute professionalizing of the quality of given functions of management. Before the advent of the sigma six methodologies, quality management in practice was mainly directed towards the production floor. The statisticians in the organization in a very separate department called the quality control department would do the assessment. With the application of the sigma six mechanisms, mainly the branch called professionalizing, all the quality controls can be monitored during the production processes. In the end, this will minimize the operational cost incurred by the company. Appendix Table1: data set to accompany problem one (i) phone name Screen size Camera Pixels Price of data Samsung Galaxy s6 5.1 16 40 Samsung Galaxy s6 edge 5.1 16 59 Samsung Galaxy s5 5.1 16 27.5 Samsung galaxy note 4 5.7 16 37.5 Samsung Galaxy s3 Mini 4 5 7.5 Samsung Galaxy s5 Mini 4.5 8 18.5 Samsung Galaxy s4 Mini 4.3 8 16.99 Samsung Galaxy alpha 4.7 12 27.5 Galaxy s5 Mini 4.5 8 18.5 Samsung Galaxy A5 5 13 26 Samsung galaxy core prime 4.5 5 13 Samsung Galaxy s3 neo 4.8 8 15 Samsung galaxy ace 4 4.3 4.3 13 Samsung galaxy young 3.27 3.15 9.5 Source: www. carphonewarehouse.com References De Feo, Joseph A.; Barnard, William., 2005. JURAN Institutes Six Sigma Breakthrough and Beyond - Quality Performance Breakthrough Methods. Tata McGraw-Hill Publishing Gujarati, D., 2008. Basic econometrics. New York: McGraw-Hill. Harry, Mikel J.; Mann, Prem S.; De Hodgins, Ofelia C.; Hulbert, Richard L.; Lacke, Christopher J., 2011).Practitioner’s guide to statistics of learn sigma six for process improvement John Wiley and Sons. pp. 30 Miller, H., 1995. Descriptive statistics. London: Open Learning Foundation Webber, Larry; Wallace, Michael (15 December 2006).Quality control for dummies. pp. 292–. Read More