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Further Readings:
Corfield D., and J. Williamson, Foundations of Bayesianism, Kluwer Academic Publishers, 2001. Contains Logic, Mathematics, Decision Theory, and Criticisms of Bayesianism.
Lapin L., Statistics for Modern Business Decisions, Harcourt Brace Jovanovich, 1987.
Pratt J., H. Raiffa, and R. Schlaifer, Introduction to Statistical Decision Theory, The MIT Press, 1994.

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What is Business Statistics?

The main objective of Business Statistics is to make inferences (e.g., prediction, making decisions) about certain characteristics of a population based on information contained in a random sample from the entire population. The condition for randomness is essential to make sure the sample is representative of the population.

Business Statistics is the science of ‘good' decision making in the face of uncertainty and is used in many disciplines, such as financial analysis, econometrics, auditing, production and operations, and marketing research. It provides knowledge and skills to interpret and use statistical techniques in a variety of business applications. A typical Business Statistics course is intended for business majors, and covers statistical study, descriptive statistics (collection, description, analysis, and summary of data), probability, and the binomial and normal distributions, test of hypotheses and confidence intervals, linear regression, and correlation.

Statistics is a science of making decisions with respect to the characteristics of a group of persons or objects on the basis of numerical information obtained from a randomly selected sample of the group. Statisticians refer to this numerical observation as realization of a random sample. However, notice that one cannot see a random sample. A random sample is only a sample of a finite outcomes of a random process.

At the planning stage of a statistical investigation, the question of sample size (n) is critical. For example, sample size for sampling from a finite population of size N, is set at: N^½+1, rounded up to the nearest integer. Clearly, a larger sample provides more relevant information, and as a result a more accurate estimation and better statistical judgement regarding test of hypotheses.

Under-lit Streets and the Crimes Rate: It is a fact that if residential city streets are under-lit then major crimes take place therein. Suppose you are working in the Mayer’s office and put you in charge of helping him/her in deciding which manufacturers to buy the light bulbs from in order to reduce the crime rate by at least a certain amount, given that there is a limited budget?

Click on the image to enlarge it and THEN print it.
Activities Associated with the General
Statistical Thinking and Its Applications

The above figure illustrates the idea of statistical inference from a random sample about the population. It also provides estimation for the population's parameters; namely the expected value µ_x, the standard deviation, and the cumulative distribution function (cdf) F_x, s and their corresponding sample statistics, mean , sample standard deviation S_x, and empirical (i.e., observed) cumulative distribution function (cdf), respectively.

The major task of Statistics is the scientific methodology for collecting, analyzing, interpreting a random sample in order to draw inference about some particular characteristic of a specific Homogenous Population. For two major reasons, it is often impossible to study an entire population:

The process would be too expensive or too time-consuming.

The process would be destructive.

In either case, we would resort to looking at a sample chosen from the population and trying to infer information about the entire population by only examining the smaller sample. Very often the numbers, which interest us most about the population, are the mean m and standard deviation s, any number -- like the mean or standard deviation -- which is calculated from an entire population, is called a Parameter. If the very same numbers are derived only from the data of a sample, then the resulting numbers are called Statistics. Frequently, Greek letters represent parameters and Latin letters represent statistics (as shown in the above Figure).

The uncertainties in extending and generalizing sampling results to the population are measures and expressed by probabilistic statements called Inferential Statistics. Therefore, probability is used in statistics as a measuring tool and decision criterion for dealing with uncertainties in inferential statistics.

An important aspect of statistical inference is estimating population values (parameters) from samples of data. An estimate of a parameter is unbiased if the expected value of sampling distribution is equal to that population. The sample mean is an unbiased estimate of the population mean. The sample variance is an unbiased estimate of population variance. This allows us to combine several estimates to obtain a much better estimate. The Empirical distribution is the distribution of a random sample, shown by a step-function in the above figure. The empirical distribution function is an unbiased estimate for the population distribution function F(x).

Given you already have a realization set of a random sample, to compute the descriptive statistics including those in the above figure, you may like using Descriptive Statistics JavaScript.

Hypothesis testing is a procedure for reaching a probabilistic conclusive decision about a claimed value for a population’s parameter based on a sample. To reduce this uncertainty and having high confidence that statistical inferences are correct, a sample must give equal chance to each member of population to be selected which can be achieved by sampling randomly and relatively large sample size n.

Given you already have a realization set of a random sample, to perform hypothesis testing for mean m and variance s², you may like using Testing the Mean and Testing the Variance JavaScript, respectively.

Statistics is a tool that enables us to impose order on the disorganized cacophony of the real world of modern society. The business world has grown both in size and competition. Corporate executive must take risk in business, hence the need for business statistics.

Business statistics has grown with the art of constructing charts and tables! It is a science of basing decisions on numerical data in the face of uncertainty.

Business statistics is a scientific approach to decision making under risk. In practicing business statistics, we search for an insight, not the solution. Our search is for the one solution that meets all the business's needs with the lowest level of risk. Business statistics can take a normal business situation, and with the proper data gathering, analysis, and re-search for a solution, turn it into an opportunity.

While business statistics cannot replace the knowledge and experience of the decision maker, it is a valuable tool that the manager can employ to assist in the decision making process in order to reduce the inherent risk, measured by, e.g., the standard deviation s.

Among other useful questions, you may ask why we are interested in estimating the population's expected value m and its Standard Deviation s ? Here are some applicable reasons. Business Statistics must provide justifiable answers to the following concerns for every consumer and producer:

1. What is your (or your customers) Expectation of the product/service you buy (or that your sell)? That is, what is a good estimate for m ?
2. Given the information about your (or your customers) expectation, what is the Quality of the product/service you buy (or that you sell)? That is, what is a good estimate for s ?
3. Given the information about what you buy (or your sell) expectation, and the quality of the product/service, how does the product/service compare with other existing similar types? That is, comparing several m 's, and several s 's.

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Common Statistical Terminology with Applications

Like all profession, also statisticians have their own keywords and phrases to ease a precise communication. However, one must interpret the results of any decision making in a language that is easy for the decision-maker to understand. Otherwise, he/she does not believe in what you recommend, and therefore does not go into the implementation phase. This lack of communication between statisticians and the managers is the major roadblock for using statistics.

Population: A population is any entire collection of people, animals, plants or things on which we may collect data. It is the entire group of interest, which we wish to describe or about which we wish to draw conclusions. In the above figure the life of the light bulbs manufactured say by GE, is the concerned population.

Qualitative and Quantitative Variables: Any object or event, which can vary in successive observations either in quantity or quality is called a"variable." Variables are classified accordingly as quantitative or qualitative. A qualitative variable, unlike a quantitative variable does not vary in magnitude in successive observations. The values of quantitative and qualitative variables are called"Variates" and"Attributes", respectively.

Variable: A characteristic or phenomenon, which may take different values, such as weight, gender since they are different from individual to individual.

Randomness: Randomness means unpredictability. The fascinating fact about inferential statistics is that, although each random observation may not be predictable when taken alone, collectively they follow a predictable pattern called its distribution function. For example, it is a fact that the distribution of a sample average follows a normal distribution for sample size over 30. In other words, an extreme value of the sample mean is less likely than an extreme value of a few raw data.

Sample: A subset of a population or universe.

An Experiment: An experiment is a process whose outcome is not known in advance with certainty.

Statistical Experiment: An experiment in general is an operation in which one chooses the values of some variables and measures the values of other variables, as in physics. A statistical experiment, in contrast is an operation in which one take a random sample from a population and infers the values of some variables. For example, in a survey, we"survey" i.e."look at" the situation without aiming to change it, such as in a survey of political opinions. A random sample from the relevant population provides information about the voting intentions.

In order to make any generalization about a population, a random sample from the entire population; that is meant to be representative of the population, is often studied. For each population, there are many possible samples. A sample statistic gives information about a corresponding population parameter. For example, the sample mean for a set of data would give information about the overall population mean m .

It is important that the investigator carefully and completely defines the population before collecting the sample, including a description of the members to be included.

Example: The population for a study of infant health might be all children born in the U.S.A. in the 1980's. The sample might be all babies born on 7^th of May in any of the years.

An experiment is any process or study which results in the collection of data, the outcome of which is unknown. In statistics, the term is usually restricted to situations in which the researcher has control over some of the conditions under which the experiment takes place.

Example: Before introducing a new drug treatment to reduce high blood pressure, the manufacturer carries out an experiment to compare the effectiveness of the new drug with that of one currently prescribed. Newly diagnosed subjects are recruited from a group of local general practices. Half of them are chosen at random to receive the new drug, the remainder receives the present one. So, the researcher has control over the subjects recruited and the way in which they are allocated to treatment.

Design of experiments is a key tool for increasing the rate of acquiring new knowledge. Knowledge in turn can be used to gain competitive advantage, shorten the product development cycle, and produce new products and processes which will meet and exceed your customer's expectations.

Primary data and Secondary data sets: If the data are from a planned experiment relevant to the objective(s) of the statistical investigation, collected by the analyst, it is called a Primary Data set. However, if some condensed records are given to the analyst, it is called a Secondary Data set.

Random Variable: