Question

We when run a hypothesis test, we are looking to verify a claim about a population parameter. Why is it important that we have a statistical tool to allow us to do this? For example, suppose that you were the quality control officer for a CPU manufacturer. Your job is to ensure that the CPUs your company makes meet certain performance standards so that when they are installed in iPhones they function properly and the phone company can truthfully claim that its phone will perform in certain ways. What would you do to verify that your CPUs were meeting both industry standards as well as the expectations of those companies that will purchase them for use in their products?

Answer 1

It is important to have a statistical tool with which certain parameters could be tested for sure, because every single unit produced by the firm cannot be tested, and therefore, sampling would be done. When sampling is done, effective and reliable estimates for population parameters could be approximated, and based on the sample data, decisions regarding population could be made.

In order to verify if the CPUs are meeting the standards and expectations of the company, we will plot Control Charts.

The statistical theory has been attached below:

The general idea of control chart is presented in the following images:

As far as judging the standards of the CPUs is concerned, we need to confirm whether the product conforms to the specifications laid out. Therefore, we will use a p - chart to test for fraction defectives. The statistical basis has been provided below: