TO: Bank X
FROM: Scott Hebert
DATE: April 24, 2009
SUBJECT: Survey Accuracy And Budget Constraints
In order for the executives at Bank X to determine the desirability of a credit card offering, it is necessary to estimate the mean cardholder spending per month. Bank X has requested that Information Experts conduct a survey to determine the mean with a confidence level of 98 percent and a confidence interval of plus or minus $10. In order to achieve the desired accuracy, Information Experts will need to survey 13,526 individuals. Although this is a large survey, a highly accurate result such as the one requested by Bank X requires a large sample in order to guarantee success.
Unfortunately, Bank X has implemented budget constraints that make this survey size impossible. Since it will cost $5 per sample, the anticipated budget for a survey with a confidence level of 98 percent and a confidence interval of plus or minus $10 would be $66,280. This far exceeds Bank X’s allotted $10,000 budget for this project. In order to fit within the new budget, the sample size must be reduced from 13,526 individuals to 2,000 individuals. It is important to remember that although the sample size is unrelated to the population size, it does have an impact on how accurate the results of a survey will be (Triola, 2008). In this case, reducing the number of samples to 2,000 while maintaining a confidence level of 98% will increase the range of the confidence interval. In fact, using 2,000 respondents will result in a confidence interval of plus or minus $26.01.
In order to ensure the greatest level of accuracy, the calculations made in this memo used critical values with four significant digits rather than three (Adams Six Sigma, n.d.). If the survey proceeds with this limited number of respondents, Bank X will be able to ascertain with a 98% confidence that the derived mean is within $26 of the actual mean. If this confidence interval is too large for Bank X to feel comfortable basing its business decision on, the choice must be made to increase the survey budget or choose an alternate method of research.
Adams Six Sigma. (n.d.) Standard normal distribution table to 7.5 standard deviations. Retrieved April 24, 2009.
Triola, M. F. (2008). Elementary statistics (10th ed.). Boston: Pearson.