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STAT 200 Elementary Statistics

Published : 27-Aug,2021  |  Views : 10

Question:

Select one (1) project from your working or educational environment in which you would use the confidence interval technique for the process. Next, speculate on one to two (1-2) challenges of utilizing such a technique in the process and suggest your strategy to mitigate the challenges in question.
Please also discuss the following:

Confidence interval measures how believable the data represents in a given interval. When we have very high confidence level, the interval is larger. Our confidence level reduces when the confidence interval gets smaller.

Here is a simple example. You try to shoot the target from a distance. If I make the target very large, you have high confidence that you won't miss the target. On the other hand, if I give you a very small target, you are not so confident that you will get to the target. In other words, you have less confidence level. Do you agree?

Answer:

Confidence interval refers to a descriptive range of the amount of uncertainty in relation to a sample estimating a particular parameter thereby giving a range of values that are deemed plausible as per the sampling results. A particular project where the confidence interval technique would be applicable is the determination of the true average time that individuals will be able to complete a certain task lies within a range around a sample mean. The sample is a representation of the population in the education environment (Altman, 2011). The total population has a population mean time and a population standard deviation both of whom are unknown.  Therefore, the intention of the paper is to conduct an analysis on the contribution of confidence interval technique in relation in handling various challenges that come their way. For instance, an individual can apply confidence interval technique in determining the average time that it will take him or her to accomplish a particular task (Belloc, 2016). The strategy, therefore, is considered to be vital in that it enable an individual to have a realistic time estimate of carrying out various activities thus enhancing effectiveness and efficiency of operation at any particular time.

There are certain speculative challenges attributed to the usage of the interval in the estimation of parameters (Lavrakas, 2008). First, sometimes the width might be too wide thus fueling uncertainty with regard to the actual value of a parameter underestimation, for instance, mean. Second, the multiplicity factor associated with a confidence interval is problematic in the sense that a set of statistical inferences are considered simultaneously thus increasing the number of comparisons. For example, Simultaneous consideration of 100 intervals yields 5 uncovering intervals with a 95t% confidence level (O'Gorman, 2004). Suppose the intervals show no dependence statistically, 99.4% is the probability that at least a single interval is not inclusive of the population parameter (Belloc, 2016). In this case, the challenges faced by while applying this mechanism can be reduced if an individual or organization employing this strategy should ensure that it analyzes realistic data that will enable one to get realistic figures that can lead to a justifiable solution in a tome of research (Smithson, 2003).

Certain strategies are applicable in the mitigation of the above challenges. In order to decrease the width of the confidence interval, the sample size will drive around parameter’s decrease with an increase in the number of observations (Frederic P. Miller, 2009). Further, the above-mentioned will be decreased by reducing the level of variability in the data. Generally, decreasing the variability decreases the standard deviation and consequently the margin of error. On the other hand, Multiplicity in confidence intervals is corrected using methods based on the Hochberg step-up process thereby obtaining confidence intervals that are devoid of multiplicity (Efird & Nielsen, 2008). Therefore, if the above challenges are put into consideration, the application of confidence interval technique will enable an individual fin deriving a reliable perimeter estimate thus being in a position of making a reliable decision that will enable an individual or organization in attaining the set goals and objectives effectively and efficiently within any particular time.

References

Altman, D. (2011). Statistics with confidence. [London]: BMJ Books.

Belloc, H. (1967). On. Freeport, N.Y.: Books for Libraries Press.

Belloc, H. (1967). On. Freeport, N.Y.: Books for Libraries Press.

Frederic P. Miller, A. (2009). Confidence interval. [Place of publication not identified]: Vdm Pub. House.

Lavrakas, P. (2008). Encyclopedia of survey research methods. Thousand Oaks, Calif.: SAGE Publications.

O'Gorman, T. (2004). Applied adaptive statistical methods. Philadelphia, PA: Society for Industrial and Applied Mathematics.

Smithson, M. (2003). Confidence intervals. Thousand Oaks, Calif.: SAGE.

Efird, J.T. and Nielsen, S.S., 2008. A method to compute multiplicity corrected confidence intervals for odds ratios and other relative effect estimates. International journal of environmental research and public health, 5(5), pp.394-398.

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