Calculating the size of the sample requires the use of sample mean and the population mean. Thus, let the sample mean be represented by letter M and the population mean be represented by letter U. the ninety five percent (95%) confidence interval is represented by the following expression m-1.96s/sqrt(n) < u < m+1.96s/sqrt(n). In the expression n represents the size of the sample used in the analysis. In this analysis, the standard deviation is $850 and the error required is $65. This is because the variation allowed is of plus or minus sixty-five dollars. In the expression, this error is 1.96s/sqrt (n). Therefore, .96(850/sqrt(n))=65. Making n the subject of the formulae and simplifying where necessary gives the value of n as 657. The value of n is large. Hence, it is not important to check whether the data is normally distributed as per the requirement of the central limit theory. The value of n gives the number of card holders to be sampled in the research as 657 (Belle, 2002).
The managers of universal credit Inc. wishes to reduce the size of the sample so that the cost of analysis may be within their budget. Decreasing the size of the sample decreases the cost of the analysis because there is a positive correlation between the cost of analysis and sample size. Also, lowering the sample size decreases the level of confidence associated with the results of the analysis (Cruz, 2002). This means that the confidence interval will widen as the sample size falls. Thus, decreasing the number of cards to be used makes the sample a bad estimate of the entire population. It is, therefore, advisable for Universal Credit Production development team to allocate adequate funds to the project to avoid decreasing the sample size (Giffen, Higgs & Yule, 2003).
References
Belle, G. V. (2002). Statistical rules of thumb. New York: Wiley-Interscience.
Cruz, M. G. (2002). Modeling, measuring and hedging operational risk. New York: John Wiley
& Sons.
Giffen, R., Higgs, H., & Yule, G. U. (2003). Statistics. London: Macmillan and.
