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  More on this in technical papers by Minitab, ref 2. Minitab Technical Assistance, ref 3, is developed to guide the user on unusual data, normality and sample size check. Minitab assistance is available for limited tests, basic statistical tests. Test assumptions for basic statistical tests like Z-test, t-test, correlation, variance, normality and outlier test can be found in Ref 4. Test assumptions for quality and process improvement tests like MSA, Control Charts, Acceptance sampling and capability analysis can be found in Ref 5. Test assumptions for Statistical modeling tools like ANOVA, Regression, DoE, Predictive analytics, Reliability and Multivariate can be found in Ref 6. Test assumptions for Predictive Analytics tools like CART, TreeNet, Random Forest and MARS can be found in Ref. 6. Test assumptions for Multivariate methods like PCA, Factor Analysis, Item Analysis, K-mean Cluster, Discriminant analysis and Correspondence analysis can be found in Ref.6. Normality assu...

  The margin of error depends on the confidence level. Confidence level is often considered the probability that the calculated confidence interval estimate will contain the true population parameter. Reference: 7.2 Confidence Intervals for a Single Population Mean with Known Population Standard Deviation – Introduction to Statistics (pressbooks.pub)

The logic of hypothesis testing is a specific application of decision theory, and it gives a normative or prescriptive idea of optimal decisions under uncertainty.  When we need to take decision/ conclude on hypothesis about a population,  we're going to be take a small sample and make a decision.  In this case we have considerable uncertainty. We don't know on the basis of our small samples whether what we're assuming is true in the population is actually accurate. In order to never be wrong we would have to measure an entire population that's not possible in most cases. Thus, scientific method for testing claim about population is required. Hypothesis test is a statistical method that uses sample data to evaluate a hypothesis about a population. S o, hypothesis test is really a set of rules that if scientists follow, we can be optimal in our decisions. In Hypothesis test, the null hypothesis s tates something very specific that in the population , for eg. population m...

Logic of Hypothesis testing goes more inline with the Falsification principle, proposed by Karl Popper. It suggests that for theory to be considered scientific, it must be able to be tested and conceivably proven false. For example, the hypothesis that 'all swans are white' can be falsified by observing a black swan'. Central question in the philosophy of science was distinguishing science from non-science. For Popper, science should attempt to disprove a theory rather than attempt to continually support theoretical hypotheses. Popper replaced inductive reasoning with deductive reasoning for distinguishing scientific theory from non-science, as we do not observe the universe at all times and in all places. Inductive Reasoning: observation > pattern > hypothesis > theory Deductive Reasoning: theory > hypothesis > observation > confirmation Poppers’ point is, no matter how many observations are made which confirm a theory, there is always the possibility tha...