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Extra info for Real-World Problems for Sec. School Math. Students
The idea of a scenario helps to explore a real situation as shown in section 1. The case of taking out an insurance policy for a car is analysed to some detail in Borovcnik (2006). There is a need for a reference concept wider than the frequentist approach. The perspective of modelling will help to explore issues. In modelling, it is rarely the case that one already knows all relevant facts from the context. Several models have to be used in parallel until one may compare the results and their inherent assumptions.
On the contrary, the usual examination as to whether a specific distribution is an adequate model for a situation is performed by a statistical test on whether the data is compatible with what is to be ‘expected’ from a random sample of this model or not. Such tests focus on the ‘external’ phenomenon of frequencies as observed in data. a. Binomial Distribution – Repeated Independent Trials A Bernoulli process may be represented by drawing balls from an urn where there is a fixed proportion p of balls marked by a 1 (success) and the rest marked by a 0 (failure).
Firstly, by common sense, no one would compare away scores to all scores in order to find differences between the two groups of trials away and home. Secondly, as the overall strength is estimated, it could also be estimated by the separate scores of away and home matches using equation (31): pˆ A and pˆ H are combined to an estimate pˆ 0 of p0. And the test would be performed by the data on away matches, which coincide with 231 = n A ⋅ pˆ A . Confusing here is that pA is dealt with as unknown (a test is performed whether it is lower than the overall strength), an estimate of it is used to get an estimate of the overall strength, and it is used as known data to perform the test.