A common practice now is for large retail pharmacies to buy the customer base from smaller, independent pharmacies. The way this works is that the buyer requests to see the customer list along with the buying history. The buyer then makes an offer based on its projection of how many of the seller's customers will move their business to the buyer's pharmacy and on how many dollars of new business will come to the buyer as a result of the purchase. Once the deal is made, the buyer and seller usually send out a joint letter to the seller's customers explaining the transaction and informing them that their prescription files have been transferred to the purchasing company.
The problem is that there is no guarantee regarding what proportion of the existing customers will make the switch to the buying company. That is the issue facing Heidi Fendenand, acquisitions manager for SaveMor Pharmacies. SaveMor has the opportunity to purchase the 6,780-person customer base from Hubbard Pharmacy in San Jose, California. Based on previous acquisitions, Heidi believes that if 70% or more of the customers will make the switch, then the deal is favorable to SaveMor. However, if 60% or less make the move to SaveMor, then the deal will be a bad one and she would recommend against it.
Quincy Kregthorpe, a research analyst who works for Heidi, has suggested that SaveMor take a new approach to this acquisition decision. He has suggested that SaveMor contact a random sample of 20 Hubbard customers telling them of the proposed sale and asking them if they will be willing to switch their business to SaveMor. Quincy has suggested that if 15 or more of the 20 customers indicate that they would make the switch, then SaveMor should go ahead with the purchase. Otherwise, it should decline the deal or negotiate a lower purchase price.
Heidi liked this idea and contacted Cal Hubbard, Hubbard's owner, to discuss the idea of surveying 20 randomly selected customers. Cal was agreeable as long as only these 20 customers would be told about the potential sale.
Before taking the next step, Heidi met with Quincy to discuss the plan one more time. She was concerned that the proposed sampling plan might have too high a probability of rejecting the purchase deal even if it was a positive one from SaveMor's viewpoint.
On the other hand, she was concerned that the plan might also have a high probability of accepting the purchase deal when in fact it would be unfavorable to SaveMor. After discussing these concerns for over an hour, Quincy finally offered to perform an evaluation of the sampling plan.
Questions:
Compute the probability that the sampling plan will provide a result that suggests that SaveMor should reject the deal even if the true proportion of all customers who would switch is actually 0.70.
Compute the probability that the sampling plan will provide a result that suggests that SaveMor should accept the deal even if the true proportion of all customers who would switch is actually only 0.60.
Write a short report to Heidi outlining the sampling plan, the assumptions on which the evaluation of the sampling plan has been based, and the conclusions regarding the potential effectiveness of the sampling plan. The report should make a recommendation about whether Heidi should go through with the idea of using the sampling plan.