The Intermountain Long Board Company is a small manufacturing company that produces about 100,000 long boards each year. Part of their manufacturing process involves receiving pre-build wheel assemblies from three different vendors. One of their vendors, Eastside Factories, is also a small manufacturer in the area and has been supplying the wheel assemblies to Intermountain for 8 years. There is a contract between Intermountain and Eastside stating that the shipments from Eastside will contain no more than 3% defective wheel assemblies. Eastside has been an excellent vendor and has helped Intermountain become a successful producer of long boards.

Bill Hernandez is the production manager at Intermountain and has taken over the position two months ago. He sends out a memo stating that the last shipment of 5,000 wheel assemblies from Eastside is totally unacceptable. He looked at a sample of 10 wheel assemblies out of the first box of the shipment and 2 were defective. That is 20% and the contract states no more than 3% is allowed. Bill is furious and wants to return the entire shipment.

You are the procurement manager and Karla Palmer, the president of Intermountain has called you to ask for help. She knows the past importance of Eastside to the company and would like to defuse the situation. Being well versed in statistics, you realize that the sample Bill took is very small and not at all random. You complete a much more thorough analysis, taking a random sample of 100 and finding 4 defective. The 95% confidence interval 3.936% to 4.064% defective. The p-value of the hypothesis test yields 0.00531. This means that we are 99.5% certain that the shipment is over the contract allowance, but not nearly as far over as Bill believes.

Write an email to Bill and Karla that does the following:

1. Convince them to accept the shipment.

2. Explain the extent of the problem with Eastside and what you concluded from your analysis.

3. Present some suggestions on how to inform Eastside of the issue without damaging the strong relationship between the companies.

***My main concern here is whether I need to conduct a hypothesis test in excel or not?