Testing the hypothesis of the normality of the falling number of oatmeal in small samples

Abstract

Verification of the hypothesis of the normality of small samples is required to establish whether the empirical distribution obtained belongs to the theoretical distribution. The condition for testing the hypothesis of normality for a set of small independent samples is the presence of a sufficient number of them with the same volume. In this case, it is possible to test the hypothesis of the normality of the general aggregates from which the studied samples were taken, assuming that the parameters of these aggregates have different values. When testing the hypothesis of normality for a large number of small samples, only one value of the first, second, etc. measurements is randomly selected from each sample, thereby allowing simplification and random selection of data. The object of this study is small samples of the falling number of oat flour used in bakery production in the development of bakery products. The purpose of this work was to test the hypothesis of normality for small samples of the experiment using the nonparametric criterion of agreement ω2 of the smallest of each of the four definitions of the incidence number, since rounding the values of direct measurements excludes the random nature of the quantity or its normal distribution in favor of a uniform one. It was found that at a significance level of p = 0?05, the table value (nω2)1-p is greater than the calculated value of nω2 for all four definitions, hence the hypothesis of the normal distribution of small samples for all four definitions (as random variables) of the falling number of oatmeal does not deviate. The results obtained in this work are consistent with the generally accepted classical concepts of testing the statistical hypothesis of the normal distribution of samples. The statistical method provides sufficient accuracy of the studied indicator in technical systems and does not require the synthesis of a statistical criterion to test the hypothesis of the normality of small sample.