08 TEST FOR PROPORTIONS, BINOMIAL DISTRIBUTION

08 TEST FOR PROPORTIONS, BINOMIAL DISTRIBUTION
In the 8th Minitab tutorial, we are in the skateboard deck production shop floor. Here in a fully automated production process, several layers of wood are pressed together under high pressure with water-based glue and special epoxy resin to form a skateboard deck. Our task in this Minitab tutorial will be to use the so-called hypothesis test, t-test for proportions, to draw a statistically indirect conclusion about the production population, in order to be able to make a statement about the error rate of the production population, with 95% certainty on the basis of the sample. For this purpose, we will subject a certain quantity of randomly selected skateboard decks to a visual surface inspection, and depending on their visual appearance, assess the skateboard decks as good or bad parts in terms of customer requirements. Good parts would be skateboard decks that meet all visual customer requirements, and correspondingly bad parts would be skateboard decks, that do not meet the visual customer requirements, and would either have to be subsequently repaired at great expense, or scrapped. Our task in the first step will be, to define the boundary conditions for the corresponding weekly sample, in order to draw an indirect conclusion in the second step, based on the error rate of our sample to the error rate in the population by using the correct hypothesis test. The special feature in this training unit will be, that we will be dealing with categorical quality judgments, in which the laws of binomial distribution rather than Gaussian normal distribution are applied. In this Minitab tutorial we will therefore get to know this binomial distribution in more detail, and also carry out the associated discriminatory power analysis for binomially distributed data, in order to determine the appropriate sample size. With this necessary preliminary work, we can then properly perform the so-called hypothesis test, test for proportions, in order to be able to make a 95% reliable recommendation for action to the management of Smartboard Company, based on our sample test results, which relates to the basic production population.

MAIN TOPICS MINITAB TUTORIAL 08

• 1-Sample t-test for proportions
• Understanding the binomial distribution
• Deriving the probability distribution of the binomial distribution
• Perform discriminatory power analysis for binomially distributed data
• Normal approximation in the context with the binomial distribution
• Working with the „tally individual variables“ function
• Sample size as a function of the discrimination quality
• Formulation of the null hypothesis and alternative hypothesis