The distribution models reflect a statistician’s assumption on how variable values are possibly distributed in a population. Based on sample data and assumptions on the population distribution, inferences are…
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Statistics use assumption on population distribution to estimate population values based on sample values (Kemp & Kemp 257-66). Probability distributions functions or simply distribution functions are used (Soong 39-41). The distribution function associates a variable value with a probability (Soong 39). This can take the form Fx(x) =P(Xx) where the lowercase x refers to a specific value of a variable. Probability distribution functions have shapes represented by the mathematical equations. The areas under the curves or distribution functions are associated with probabilities.
In business statistics, some of the distribution functions that are often used are the Z-statistics, t-statistics, chi-square distribution, and the F-statistics (Kemp & Kemp 47-297). There is also an option to use what statisticians call as the non-parametric statistics (Kemp & Kemp 298-315). The choice of what distribution functions to use are determined by convention or typical practice and theory. For example, in estimating the population mean, it is assumed that the sample mean converge to the population mean through repetition of sampling procedures or if the population is large. Thus, in estimating the mean, statistics usually makes the assumption based on a normal distribution. Although several distribution functions are used in statistics, in this work we focus our sights on three: the z-statistics, the t-statistics, and the chi-square statistics.
Figure 1 captures a standard normal distribution function. The standard normal distribution associates a value of a variable with probability. For example, the probability that the value of the variable is between a very low number and high number can be represented by 100%. In the language of statistics, this take s the form P (-< x < +) = 1 or 100%. In other words, this means that in a
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