Problem - 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 centerin 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. Using the sample estimate calculated in (a), determine the precision interval if the calculated precision were:
Precision Precision interval
1. $100,000 $ to $
2. $200,000 $ to $
3. $300,000 $ to $