In: Statistics and Probability
SaveMor Pharmacies
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, an 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.
Required Tasks:
1. (7 points) Using Minitab, 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.
Provide Minitab output of probabilities here
2. (7 points) 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.
Provide Minitab output of probabilities here
3. (6 points) 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 using the
sampling plan.
Provide your short, well-written and professional report here