Identifying population parameters is essential to the success of a research or the production process (Sharpe, DeVeaux, & Velleman, 2015). Herein the significance of the tools known as confidence intervals lies. Allowing estimating the key parameters of the target population, continence intervals serve as a means of reducing the chances for an error to occur and, therefore, have to be incorporated into every major project to improve its outcomes.

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In order to understand the difference between z and t confidence intervals, one will have to mention the nature of the concepts first. A closer look at the two phenomena under analysis will reveal that the key difference in the notions in question concerns primarily what is being calculated. In other words, z confidence interval is used when the need to calculate a confidence interval for a mean of a certain range of data is required. The t confidence interval, in its turn, is used when the necessity to identify and quantify a proportion emerges.

Apart from the issues, which the confidence intervals mentioned above help address, the scenarios, in which each of the formulas is used, are quite different from each other. For instance, the z confidence interval calculation is traditionally adopted as the means of measuring a specific sample size in the instances, when the population distribution cab be characterized as normal (Sharpe et al., 2015). The aforementioned cases embrace the scenarios, in which the total number of the sample population reaches or exceeds thirty people.

The t-confidence coefficient, in its turn, is applied to the cases, which presuppose that the number of participants should be less than the required minimum, which typically equals to thirty.

Therefore, the t-confidence coefficient can be applied to the experiments, in which the sample size is going to be comparatively small. In addition, the use of the t-distribution and, therefore, the t-coefficient presupposes that the concept of degrees of freedom should be incorporated into the analysis. The phenomenon of degrees of freedom can be defined as the number of factors that affect one or more than one variable and, therefore, altering the state of the system, in which the experiment is carried out or in which the subject of the research can exist (Katz, 2012). In other words, the changes in the degrees of freedom will trigger the corresponding alterations in the coefficient.

The z-confidence interval, in its turn, can be applied to the practical problems, which require more accurate solutions, since the z interval has a much smaller margin of errors compared to the t-confidence interval. In other words, the specified approach can be viewed as an essential addition to the production process involving working with filament materials (Katz, 2012). While the t-confidence interval also serves as a rather solid tool for identifying the required population parameters.

Since different production processes require different rates of precision, the adoption of the corresponding type of the confidence interval for the identification of the population and the error margins is essential to the outcomes. Seeing that the z-confidence interval has a much narrower margin than the abovementioned alternative, it is reasonable to suggest that it should be used in the production processes that require an increased amount of accuracy. The t-confidence interval, in its turn, can be applied to the scenarios, in which a rather generalized outcome is expected.

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## Reference List

Katz, M. H. (2012). *Multivariable analysis: A practical guide for clinicians and public health researchers*. Cambridge, Massachusetts: Cambridge University Press. Web.

Sharpe, N. D., DeVeaux, R. D., & Velleman, P. (2015). *Business statistics*. 3rd ed. Upper Saddle River, New Jersey: Pearson. Web.