Business Statistics Contemporary Decision Making

Question: Discuss about the Business Statistics for Contemporary Decision Making. Answer: Introduction: Normal distribution is a distribution of random variables, which represents the outcomes of the random variables like a symmetrical bell-shaped graph. The normal distribution depicts the graph of any random variable in a way most of the life events normally take shape. Philosophically, every person struggles in the beginning, then reaches a peak and then fall out in the later years. This phenomenon is so common that it now has been termed as normal by Gauss and any data values depicting similar distributions are coined as normal distributions. Normal distribution is continuous distribution with two parameters, Mean and variance. The mean, median and mode of the normal distribution are same. Normal distribution, in its simplest form, with 0 mean and 1 standard deviation, is called standard normal distribution. IfXis a general normal deviate, then will have a standard normal distribution (Anderson et al. 2015). Sampling distribution is the distribution of the statistic from a wide range of values of the population. For example, the sampling distribution of mean is Normal. This is because of central limit theorem, which states, Given a population with a finitemean and a finite non-zero variance 2, thesampling distributionof themeanapproaches a normaldistributionwith ameanof and a variance of as N, thesamplesize, increases. The question is what is the large sample size? Some consider it anything above 30 or some around 100. For a non-normal parent population, the sampling distribution of mean for large sample sizes, depict a bell shaped curve from the simulation, with little skewness. Since the curve can be approximated by normal distribution, with some error, normal distributions are best suited as sampling distributions (Lomax and Hahs-Vaughn 2013). Inferential statistics helps in making assumptions about the distribution of the parent population using the sample data. Most of the assumptions in the inferential statistics branch, as based on the Central limit theorem, which states that, for large sample size, the sampling distribution of mean, follow normal distribution with sample mean as the population mean and sample variance by sample size as the population variance. Its on this basis, the confidence intervals are constructed, stating with alpha percent confidence, the confidence limits would include the population parameter. Larger the sample size , the closer would be the sample estimates of the population (Black 2013). References Anderson, D., Sweeney, D., Williams, T. and Anderson, D. (2015). Essentials of modern business statistics with Microsoft Excel. 6th ed. Cengage Learning. Black, K. (2013). Business Statistics: For Contemporary Decision Making. 8th ed. Wiley Global Education. Lomax, R. and Hahs-Vaughn, D. (2013). An introduction to statistical concepts. 3rd ed. Routledge.