07 t-TEST, PAIRED SAMPLES
In the 7th Minitab tutorial, we find ourselves in the development department of Smartboard Company. As part of the manufacture of prototypes, Smartboard Company has developed two new high-performance materials made of stainless-steel powder. The powder form is necessary because the skateboard axles for the professional sector are no longer to be manufactured from die-cast aluminum as before, but using the SLM production method. SLM stands for „selective laser melting“ and is currently one of the most innovative rapid prototyping processes. In this process the stainless-steel powder is completely remelted using a laser beam and applied in three-dimensional layers under computer control. The layer-by-layer application takes place in several cycles, with the next layer of powder being remelted and applied after each solidified layer until the 3D printing of the axis is complete. During prototype development, the team worked intensively on optimizing the stainless-steel powder used for 3D printing. Accordingly, our core task in this training session will be, to find out which of these two types of stainless-steel powder has the better i.e., higher toughness properties on the basis of a random sample, and a suitable hypothesis test. The core technological parameter of toughness is determined in the unit joule and is a measure of the resistance to axle breakage or crack spreading in the skateboard axles under impact load. According to the research director’s specifications, we are to draw an indirect conclusion about the production population on the basis of a random sample, and make a 95% reliable recommendation as to whether the average toughness’s differ from each other by at least 10 joules. In the course of this training session, we will guide the quality team in finding out which material has the better toughness properties for the skateboard axles by using the so-called hypothesis test, t-test for paired samples. And in the further course of this Minitab training, we will also experience that this time we are dealing with more than two production populations. We will learn why the paired-sample t-test is the method of choice in such cases rather than the classic two-sample t-test. We will take a closer look at the formula for the t-value in the paired sample t-test, calculate the most important parameters, and compare them with the values in the output window. In this context, we will again work with the useful calculator function to determine the relevant parameters. Finally, we will perform the t-test for paired samples by using the so-called Minitab Assistant, which is particularly useful in turbulent day-to-day business to perform the correct calculations with useful decision questions.
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