Question: An investment advisor has worked with 24 clients for the past five years. Following are the percentage rates of average five-year returns that these 24 clients experienced over this time frame on their investments:
11.2 11.2 15.9 2.7 4.6 7.6 15.6 1.3 3.3 4.8 12.8 14.9
10.1 10.9 4.9 -2.1 12.5 3.7 7.6 4.9 10.2 0.4 9.6 -0.5
This investment advisor plans to introduce a new investment program to a sample of his customers this year. Because this is experimental, he plans to randomly select 5 of the customers to be part of the program. However, he would like those selected to have a mean return rate close to the population mean for the 24 clients. Suppose the following 5 values represent the average five-year annual return for the clients that were selected in the random sample:
11.2 -2.1 12.5 1.3 3.3
Calculate the sampling error associated with the mean of this random sample. What would you tell this advisor regarding the sample he has selected?