Statistical Hypotheses and Their Checking

The introduction of the formulation of the statistical hypotheses and their checking have already been presented in Section 5.2.2.1 where we proposed the analysis of the comparison between the mean values and dispersions of two selections drawn from the same population. If we consider the mean values in our actual example, the problem can be formulated as follows if xi is the mean value calculated with the values in Table 5.4 and X2 is the mean value for another selection extracted from the same population (such as for example X2, which is the limiting reactant concentration at the reactor input for Table 5.2, column 2) we must demonstrate whether Xj is significantly different from X2-A similar formulation can be established in the case of two different dispersions in two selections extracted from the same population. Therefore, this problem can also be extended to the case of two populations with a similar behaviour, even though, in this case, we have to verify the equality or difference between the mean values pj and P2 ot between the variances and Oj. We frequently use three major computing steps to resolve this problem and to check its hypotheses  

we obtain the value of a random variable associated to the zero hypothesis and to the commonly used distributions, we establish the value of the correlated repartition function, which is in fact a probability of the hypothesis existence. 

Current Comparison Zero Test used Computed Associated Condition 

We compute the current value of the Fischer random variable associated to the dispersions Sj and Sj F = Sj/sj  

We obtain the probability of the current Fischer variable by computing the value of the repartition function  

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