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In Chapter 8 of Hypothesis Test, Seventh Edition of Statistics, why does one-sided test use the critical value of 1.645 and two-sided test use the critical value of 1.96?
Chapter 8 of the seventh edition of statistics, because the hypothesis test is stipulated, the critical value for one-sided test is 1.645 and the critical value for two-sided test is 1.96.

The quantile of the standard normal distribution corresponding to the significance level of 0.05 for one-sided test is 1.645, while that of the standard normal distribution of 0.025 for two-sided test is 1.96.

When the significance level of a given test is a=0.05, the z value of bilateral test is 1.96.

When the significance level of a given test is a=0.0 1, the z value of the bilateral test is 2.58.

When the significance level of a given test is a=0.05, the z value of one-sided test is 1.645.

When the significance level of a given test is a=0.0 1, the z value of one-sided test is 2.33.

definition

Critical value refers to the condition that a physical quantity must meet when an object changes from one physical state to another, which is equivalent to stagnation point in mathematics. Therefore, it is an important method to solve the maximum and minimum values of physical quantities by using critical state. Some people think that it is prudent to solve the maximum value with critical state, and the relationship between the two States should be distinguished first.