In an individual's aspect of life, especially in a business context, there is the need to justify one's decisions on the basis of data and not guesswork. Good managerial decisions are driven by statistical skills to help the managers in intelligently gather, analyze and interpret data important in decision-making. Sampling distributions help managers solve organizational problems in a diversity of contexts, minimize guesswork and also add substance to decisions. In a competitive business environment, managers are pushed to design quality products, and during the manufacturing process, they have to employ statistical methods to provide high yields. A manager cannot control the changes in the business world, but he/she can use statistics to measure and analyze the possibilities to come with the best predication.
Sampling distribution is defined as the probability distribution of a statistic such as mean, standard deviation or proportion) in a random sample. It provides a simple way of statistical inference (Black, 2012a). If the sample size is more than 30, it is assumed to be a normal distribution. Thus the one can use the mean and the standard deviation to determine the sampling distribution. A normal distribution is perfectly symmetrical, and the statistics are all equal. Sampling distributions are important in making managerial decisions since they allow analytical considerations of a statistic rather than the joint probability distribution of each unit in a sample value (Black, 2012a).
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There are different ways of finding a confidence interval for a proportion. An example when deciding for a situation that involves the marketing manager finding a sample size of this product to use in his firm. He needs to construct a confidence interval to avoid having inadequate sample size or wasting resources with the use of too many samples. The sample size confidence level will involve the manager computing the mean and the standard deviation, then using the Microsoft Excel program to calculate the CI (Arsham, n.d).
T-statistics is used when solving problems where the sample size is small, and the population standard deviation is unknown. An example is when an individual measure the average diameter of shafts from a machine with a small sample of 15. On the other hand, Z statistics is used when the sample size is large, above 30, during the comparison of the means of two populations (Black, 2012b). Unlike T-test, one does not need to know the population standard deviation or not. An example of its application is when computing the average doctor's salaries of women versus men.
Sampling methods are divided into two groups; probability and non-probability sampling. The non-probability sampling method is further grouped into volunteer and haphazard samples which are based not on random selection, but the human choice (Black, 2012a). Probability sampling method, one can determine a sample and the units available. It can also determine the probability of each sample being selected; they guarantee that the chosen unit represents the sample size. This method is divided into; simple random sampling, stratified sampling, cluster, systematic and multistage sampling (Black, 2012a).
Microsoft Excel offers Confidence formula to compute the confidence interval, that is, the range from the value in question in which the true proportion has a probability of existing (Anderson et al., 2017). First, one enters the alpha value (1-confidence level) in cell B1, then enters the standard deviation in cell B2, in cell B3, enter the sample size, then finally enter “CONFIDENCE (B1, B2, B3)” in cell B4. Excel program will automatically display the confidence level.
The Central limit theory states that the average of one’s sample mean will be equal to the population mean as long as the sample size is large enough, especially one exceeding 30.
References
Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2017). Essentials of Modern Business Statistics with Microsoft Office Excel . Cengage Learning
Arsham, H. (n.d). Statistical Thinking for Managerial Decisions. Retrieved from https://home.ubalt.edu/ntsbarsh/Business-stat/opre504.htm
Black, K. (2012a). Sampling and Sampling Distributions. In Populations. Business statistics: For contemporary decision making . Hoboken, NJ: Wiley.
Black, K. (2012b). Statistical Inference: Estimation for Single Populations. In Populations. Business statistics: For contemporary decision making . Hoboken, NJ: Wiley.
