The Badke Foundation was set up by the Fred Badke family following his death in 2001. Fred had been a very successful heart surgeon and real estate investor in San Diego, and the family wanted to set up an organization that could be used to help less fortunate people. However, one of the concepts behind the Badke Foundation is to use the Badke money as seed money for gathering contributions from middle-class families. To help in the solicitation of contributions, the foundation was considering the idea of hiring a consulting company that specialized in this activity. Leaders of the consulting company maintained in their presentation that the mean contribution from families who actually contribute after receiving a specially prepared letter would be $20.00.
Before actually hiring the company, the Badke Foundation sent out the letter and request materials to many people in the San Diego area. They received contributions from 166 families. The contribution amounts are in the data file called Badke.
a. Assuming that these data reflect a random sample of the population of contributions that would be received, compute the sampling error based on the claim made by the consulting firm.
b. Comment on any issues you have with the assumption that the data represent a random sample. Does the calculation of the sampling error matter if the sample is not a random sample? Discuss.