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The Intermountain Long Board Company is a small manufacturing company that produces about 100,000 long boards...

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?

Solutions

Expert Solution

To address your main concern: You need not conduct anhy hypothesis test here. The test has already been conducted and results summarized in the case itself. So you need not test any further.

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The email:

Dear Bill and Karla,

Trust this mail finds you in good health. Hope you are taking all precautions in this time of pandemic and all your family members are safe.

I have looked into the last shipment of 5,000 wheel assemblies from Eastside. At the outset, I just want to bring to your notice the results of my hypothesis testing:

  • I took a random sample of 100 and found 4 of them to be defective.
  • The 95% confidence interval was 3.936% to 4.064% defective.
  • The p-value of the hypothesis test yielded 0.00531 thereby making me conclude that we are 99.5% certain that the shipment is indeed over the contract allowance.
  • However, the situation is not that bad.

While a similar test was done by Bill in the past, I believe the sameple size chosen was just 10 of which 2 were defective. While samples were chosen, the methodology of selection didn't ensure random selection. Also a sample size of 10 was too small to give any statistically meaningful results.

Nevertheless, the fact that the shipment is indeed over the contract allowance, can't be debated. However, we need to understand the fact that Eastside had been our reputed and trusted suppliers since so many years in the past. We should therefore not reject the entire lot. This will lead to a significant loss to them.

We need to work out a middle path to resolve this. We can manually examine each of the 5000 pieces and accep the acceptable ones. After all, there are just 5,000 of them. We can then return the defective ones to Eastside and request them to reverse the invoice to reflect the accepted quantity only. This way their losses can be curtailed and our relationship can strengthen further.

We can discuss this with Eastside and make them aware of what we are thinking. I am sure, Eatside will also be agreeable to this idea.

What do you guys think about this? Please do let me know.

Regards.

XXX


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