A social service agency plans to conduct a survey to determine the mean income of its clients. The director of the agency prefers that you measure the mean income very accurately, to within + or - $500 from a sample taken 2 years ago, you estimate that the standard deviation of income for this population is about $5000 your job is to figure out the necessary sample size to reduce the confidence interval to +/- $500
a. What sample size should be drawn to meet the director's requirement at the 95% level of confidence?
b. What sample size should be drawn to meet the director's requirement at the 99% level of confidence?
The solution provides step by step method for the calculation of sample size. Formula for the calculation and Interpretations of the results are also included.