Question: Sample Evaluation. Marts Inc., a local fund-raising organization, is considering the feasibility of a fund-raising campaign to assist a youth organization in building a new recreation center in College Bryan, Texas. Marts has been asked to determine whether this campaign would be successful in raising $1.5 million, the amount needed to construct and equip the center. Because unsuccessful fund-raising efforts have a negative impact on Marts' ability to obtain future clients and engagements, it has established a reliability of 99 percent; that is, Marts wants to have a very high level of confidence that the $1.5 million can be successfully raised in the local community. Because a total of 50,000 citizens live in the College Bryan area, the average gift necessary to ensure a successful campaign is $30 per person ($1,500,000 ÷ 50,000). Based on the sampling risk associated with 99 percent reliability, Marts determined a sample size of 200 and surveyed each of these individuals with respect to their willingness to donate to the fund- raising campaign. The average level of support indicated by these 200 persons was $35 per person.
Required: a. Based on Marts's sample, calculate the sample estimate for the total amount that could be raised under this fund-raising effort.
b. Based only on the sample estimate, how would you advise Marts as to the potential success of its fund-raising campaign?
c. What is the primary limitation to Marts in making its decision based only on the sample estimate?
d. What is sampling risk? What types of factors could influence Marts's exposure to sampling risk in this particular situation?
e. Using the sample estimate calculated in (a), determine the precision interval if the calculated precision were
1. $100,000.
2. $200,000.
3. $300,000.
f. How would you advise Marts regarding the potential success of the fund-raising campaign based on the precision intervals calculated in (e)?
g. Assume that Marts believes that 99 percent reliability is too stringent and is considering lowering the reliability to 95 percent. How will this change affect the precision interval and the likelihood that Marts will conclude that the fund-raising campaign will ultimately be successful?