The Noun Interpretation of Statistical Inference

Statistical inference is a probabilistic inference based on random observation data (samples) and the conditions and assumptions (models) of the problem. It is the main task of mathematical statistics, and its theory and method constitute the main content of mathematical statistics. The purpose of statistical inference is to use the basic assumptions of the problem and the information contained in the observation data to make as accurate and reliable a conclusion as possible. Periodic systematic sampling, also known as equidistant sampling or mechanical sampling, is to sequentially number the population, determine the first block by drawing lots or looking up a random number table, and then take samples in turn according to the principle of equidistant sampling. When the same product is produced by different equipment and different environments, the quality of the product may vary greatly due to different conditions. In order to make the sampled samples representative, the products produced under different conditions can be grouped to make the products in the same group have the same quality, and then the samples in each group are randomly selected in proportion to synthesize a sample.

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A basic feature of statistical inference is that the conditions it is based on contain random observation data. Probability theory takes random phenomena as the research object and is the theoretical basis of statistical inference.

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In mathematical statistics, the problem of statistical inference is often manifested in the following forms: the problem studied has a definite population, and its overall distribution is unknown or partially unknown, and some conclusions related to the unknown distribution are drawn through the samples (observation data) extracted from the population. For example, the height of a group of people constitutes a whole, and it is generally believed that the height obeys a normal distribution, but the average value of this whole is unknown. Randomly select some people to measure their height, and use these data to estimate the average height of this group of people. This is a form of statistical inference, that is, parameter estimation. If the question of interest is "Does the average height exceed 1.7 (m)", it is necessary to test whether this proposition is true through samples, which is also a form of reasoning, that is, hypothesis testing. Because statistical inference infers the whole (population) from parts (samples), it cannot infer the whole from samples, and its conclusion should be expressed in the form of probability. The purpose of statistical inference is to use the basic assumptions of the problem and the information contained in the observation data to make as accurate and reliable a conclusion as possible.

Statistical inference is to extract some samples from the population, and then make a scientific judgment on the population through reasonable analysis of the random data obtained from the extracted part. It is accompanied by a certain probability of speculation, and its characteristics are: the population is inferred from the sample, and statistical inference is the core part of mathematical statistics. The basic problems of statistical inference can be divided into two categories: one is parameter estimation; The other is hypothesis testing.