Selection Of Optimal Significance Level α On Statistical Hypothesis Test

Hypothesis testing which is a method that inferred the populationfrom the sample based on certain assumptions in mathematical statistics,as a important part of statistics inference, has always received the greatattention and been widely used. In the process of statistical testing, thetraditional choice of the value of α which is significance level is0.01,0.05and0.1, however, when it mentioned to how to decide the α in generaldomestic and foreign mathematical statistics books, they always said youcan combine with the actual situation and didn’t tell you how to do it.In the existing research of scholars from home and abroad, how todecide the significance level in hypothesis testing is always depended onthe population mean, population variance or a hypothesis testing to therelationship between some two samples, currently almost no people havea more detailed discussion about how to decide the α in the case ofsample proportion Hypothesis testing. However, in some cases(polls,surveys, elections and so on,...), the existing literature still choose thesignificance level α of0.01,0.05and0.1, but by computer statisticalsimulation, I find in this case if we still choose a smaller α, there will be agreat misjudgments.On the basis of the summary of the existing literature achievements,this paper mainly expands from the following parts, the first part gives asummary on hypothesis testing and significance level; the second part mainly introduces the meaning of significance level alpha and the valueof probability in hypothesis testing; the third part mainly investigates howto decide the value of alpha with a given sample size n and sampleproportion pi; the fourth part works out an alpha distribution table andworks up a model, and gives some cases and analyzes them; the last partintroduces the conclusions, deficiency and future work of this paper.Thus, the paper simulates hypothesis testing which sets variouskinds of parameters comprehensively under different conditions by usingstatistical simulation. When having hypothesis testing for the sampleproportion, by the thorough discussion of how to decide the significancelevel alpha under different sample size and different proportion ofsampling we find: when choosing the traditional significance alpha, thelager the sample size, the smaller the probability of making mistake, thehigher the accuracy. I work out an alpha distribution table according tothis, expecting to provide a scientific method and important reference forchoosing proper significance level on such types of hypothesis testing instatistical analysis.