Abstract
Assuming that the test is one of the main contents of the statistical inference, it is widely used, and almost all of the major fields use hypothesis test, a statistical idea, and in the process of hypothesis testing, we need to construct a reasonable test statistic. Therefore, based on the hypothesis test and the knowledge of the central limit theorem, we construct a new test statistic when the sample size is sufficiently large, This statistic makes the calculation of the original test problem easier. This paper verifies the rationality of this test statistic by an example.
Highlights
One of the basic problems of mathematical statistics[1] is to take samples from the population to be observed or experimental, according to the limited information obtained on the whole to infer the problem, each inference must be accompanied by a certain probability to show the reliability of the inferred, This inference with a certain probability is called statistical inference, and one of the main aspects of statistical inference is the statistical hypothesis test
[1] it is important to assume that the test is an important part of mathematical statistics, and that the test statistic is important in this process
We are looking for a large sample test for the following three types of hypothesis testing: (θ is known in practical problems)
Summary
One of the basic problems of mathematical statistics[1] is to take samples from the population to be observed or experimental, according to the limited information obtained on the whole to infer the problem, each inference must be accompanied by a certain probability to show the reliability of the inferred, This inference with a certain probability is called statistical inference, and one of the main aspects of statistical inference is the statistical hypothesis test. [1] it is important to assume that the test is an important part of mathematical statistics, and that the test statistic is important in this process. Hypothetical test [2] is the basic common statistical methods, it is an important teaching content in the course of "probability theory and mathematical statistics". Yang Gang [3] first demonstrated the basic idea of hypothesis testing, he given us a reasoning and derivation process for rejecting domain and accepted domain in the one sided test and two-sided test of Population parameter, and showing an application example. For the large sample test construct in the course of "probability theory and mathematical statistics". The existing literature examines how to conduct hypothetical tests from different perspectives, making it easier for readers to accept and understand hypothesis testing. This paper attempts to start from the large sample test [6], to provide a new test statistics, broaden the reader's vision
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